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SPIRES-BOOKS: FIND KEYWORD MEASURE AND INTEGRATION *END*INIT* use /tmp/qspiwww.webspi1/10473.6 QRY 131.225.70.96 . find keyword measure and integration ( in books using www Cover
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Call number:0471179787:ONLINE Show nearby items on shelf
Title:Lebesgue Measure and Integration: An Introduction
Author(s): Burk
Date:1997
Publisher:Wiley-Interscience
Size:1 online resource (313 p.)
ISBN:9780471179788
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:0471042226:ONLINE Show nearby items on shelf
Title:The Elements of Integration and Lebesgue Measure
Author(s): Bartle
Date:1995
Publisher:Wiley-Interscience
Size:1 online resource (180 p.)
ISBN:9780471042228
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:047025954X:ONLINE Show nearby items on shelf
Title:Measure and Integration: A Concise Introduction to Real Analysis
Author(s): Richardson
Date:2009
Publisher:Wiley
Size:1 online resource (238 p.)
ISBN:9780470259542
Series:eBooks
Series:Wiley Online Library
Series:Wiley 2016 package purchase
Keywords: Mathematics
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Call number:SPRINGER-2016-9789462392014:ONLINE Show nearby items on shelf
Title:Spaces of Continuous Functions
Author(s): G.L.M Groenewegen
Date:2016
Size:1 online resource (173 p.)
Note:10.2991/978-94-6239-201-4
Contents:Topological Preliminaries -- Metrizable Compact Spaces -- The Stone-Weierstrass Theorem -- Weak Topologies. The Alaoglu Theorem -- Riesz Spaces -- Yosida’s Representation Theorem -- The Stone-Čech compactification -- Evaluations -- C(X) determin es X -- The Riesz Representation Theorem -- Banach Algebras -- Other Scalars
ISBN:9789462392014
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Atlantis Studies in Mathematics: 4
Keywords: Mathematics , Functional analysis , Measure theory , Mathematics , Functional Analysis , Measure and Integration
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Call number:SPRINGER-2016-9783319335728:ONLINE Show nearby items on shelf
Title:Open Problems in the Geometry and Analysis of Banach Spaces
Author(s): Antonio J Guirao
Date:2016
Size:1 online resource (169 p.)
Note:10.1007/978-3-319-33572-8
Contents:Preface -- Basic linear structure -- Basic linear geometry -- Biorthogonal systems -- Smoothness, smooth approximation -- Nonlinear geometry -- Some more nonseparable problems -- Some applications -- Bibliography -- List of concepts and problems -- Symbol index -- Subject index.
ISBN:9783319335728
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Approximation theory , Functional analysis , Measure theory , Convex geometry , Discrete geometry , Algebraic topology , Mathematics , Functional Analysis , Approximations and Expansions , Measure and Integration , Convex and Discrete Geometry , Algebraic Topology
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Call number:SPRINGER-2016-9783319335070:ONLINE Show nearby items on shelf
Title:Monte Carlo and Quasi-Monte Carlo Methods MCQMC, Leuven, Belgium, April 2014
Author(s):
Date:2016
Size:1 online resource (57 p.)
Note:10.1007/978-3-319-33507-0
Contents:Part I Invited papers -- Multilevel Monte Carlo Implementation for SDEs driven by Truncated Stable Processes -- Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo -- Vandermonde Nets and Vandermonde Sequences -- Path Space Markov Chain Monte Carlo Methods in Computer Graphics -- Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC -- Some Results on the Complexity of Numerical Integration -- Approximate Bayesian Computation: A Survey on Recent Results -- Part II Contributed papers -- Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier–Stokes Equations -- Unbiased Simulation of Distributions with Explicitly Known Integral Transforms -- Central Limit Theorem for Adaptive Multilevel Splitting Estimators in an Idealized Setting -- Comparison between LS-Sequences and β -adic van der Corput Sequences -- Computational Higher Order Quasi-Monte Carlo Integration -- Numerical
Computation of Multivariate Normal Probabilities using Bivariate Conditioning -- Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations -- On ANOVA Decompositions of Kernels and Gaussian Random Field Paths -- The Mean Square Quasi-Mont e Carlo Error for Digitally Shifted Digital Nets -- Uncertainty and Robustness in Weather Derivative Models -- Reliable Adaptive Cubature Using Digital Sequences -- Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives -- Adaptive Multidimensional Integration Based on Rank-1 Lattices -- Path Space Filtering -- Tractability of Multivariate Integration in Hybrid Function Spaces -- Derivative-based Global Sensitivity Measures and Their Link with S obol’ Sensitivity Indices -- Bernstein Numbers and Lower Bounds for the Monte Carlo Error -- A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes -- A Strategy for Parallel
Implementations of Stochastic Lagrangian Simulation -- A New Rejection Sampling Method for Truncated Multivariate Gaussian Random Variables Restricted to Convex Sets -- Van der Corput and Golden Ratio Sequences Along the Hilbert Space-Filling Curve -- Uniform Weak Tractability of Weighted Integration -- Incremental Greedy Algorithm and Its Applications in Numerical Integration -- On “Upper Error Bounds for Quadrature Formulas on Function Classes” by K K Frolov -- Tractability of Function Approxi mation With Product Kernels -- Discrepancy Estimates for Acceptance-Rejection Samplers Using Stratified Inputs -- List of Participants -- Index
ISBN:9783319335070
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Springer Proceedings in Mathematics & Statistics: 163
Keywords: Mathematics , Applied mathematics , Engineering mathematics , Computer mathematics , Mathematics , Computational Mathematics and Numerical Analysis , Applications of Mathematics
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Call number:SPRINGER-2016-9783319310893:ONLINE Show nearby items on shelf
Title:Brownian Motion, Martingales, and Stochastic Calculus
Author(s): Jean-François Le Gall
Date:2016
Size:1 online resource (1 p.)
Note:10.1007/978-3-319-31089-3
Contents:Gaussian variables and Gaussian processes -- Brownian motion -- Filtrations and martingales -- Continuous semimartingales -- Stochastic integration -- General theory of Markov processes -- Brownian motion and partial differential equations -- Stoch astic differential equations -- Local times -- The monotone class lemma -- Discrete martingales -- References
ISBN:9783319310893
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Graduate Texts in Mathematics: 274
Keywords: Mathematics , Measure theory , Economics, Mathematical , System theory , Mathematical models , Probabilities , Mathematics , Probability Theory and Stochastic Processes , Quantitative Finance , Measure and Integration , Mathematical Modeling and Industrial Mathematics , Systems Theory, Control
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Call number:SPRINGER-2016-9783319307442:ONLINE Show nearby items on shelf
Title:Real Analysis
Author(s): Peter A Loeb
Date:2016
Size:1 online resource (274 p.)
Note:10.1007/978-3-319-30744-2
Contents:Preface -- Set Theory and Numbers -- Measure on the Real Line -- Measurable Functions -- Integration -- Differentiation and Integration -- General Measure Spaces -- Introduction to Metric and Normed Spaces -- Hilbert Spaces -- Topological Spaces -- Measure Construction -- Banach Spaces -- Appendices -- References.
ISBN:9783319307442
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Measure theory , Functions of real variables , Mathematics , Real Functions , Functional Analysis , Measure and Integration
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Call number:SPRINGER-2016-9783319306209:ONLINE Show nearby items on shelf
Title:Introduction to Probability with Statistical Applications
Author(s): Géza Schay
Date:2016
Edition:2nd ed. 2016
Size:1 online resource (385 p.)
Note:10.1007/978-3-319-30620-9
Contents:Introduction -- The Algebra of Events -- Combinatorial Problems -- Probabilities -- Random Variables -- Expectation, Variance, Moments -- Some Special Distributions -- The Elements of Mathematical Statistics
ISBN:9783319306209
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Mathematical statistics , Measure theory , Applied mathematics , Engineering mathematics , Probabilities , Statistics , Mathematics , Probability Theory and Stochastic Processes , Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Scien , Probability and Statistics in Computer Science , Measure and Integration , Applications of Mathematics
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Call number:SPRINGER-2016-9783319295350:ONLINE Show nearby items on shelf
Title:The Method of Rigged Spaces in Singular Perturbation Theory of Self-Adjoint Operators
Author(s): Volodymyr Koshmanenko
Date:2016
Size:1 online resource (237 p.)
Note:10.1007/978-3-319-29535-0
Contents:Preface -- Introduction -- 1.Preliminaries -- 2.Symmetric Operators and Closable Quadratic Forms -- 3.Self-adjoint Extensions of Symmetric Operators -- 4.Rigged Hilbert Spaces -- 5.Singular Quadratic Forms -- 6.Dense Subspaces in Scales of Hilbert Spaces -- 7.Singular Perturbations of Self-adjoint Operators -- 8.Super-singular Perturbations -- 9.Some Aspects of the Spectral Theory -- References -- Subject Index -- Notation Index
ISBN:9783319295350
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Series:Operator Theory: Advances and Applications: 253
Keywords: Mathematics , Measure theory , Operator theory , Mathematical physics , Mathematics , Operator Theory , Measure and Integration , Mathematical Applications in the Physical Sciences
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Call number:SPRINGER-2016-9783319290461:ONLINE Show nearby items on shelf
Title:Measure and Integration
Author(s): Hari Bercovici
Date:2016
Edition:1st ed. 2016
Size:1 online resource (300 p.)
Note:10.1007/978-3-319-29046-1
Contents:Rings of sets -- Measurability -- Integrals and Measures -- Convergence Theorems for Lebesgue Integrals -- Existence and Uniqueness of Measures -- Signed Measures, Complex Measures and Absolute Continuity -- Measure and Topology -- Product Measures -- The Lp Spaces -- Fourier Analysis -- Standard Measure Spaces.
ISBN:9783319290461
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Measure theory , Functions of real variables , Mathematics , Measure and Integration , Real Functions
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Call number:SPRINGER-2016-9783319278735:ONLINE Show nearby items on shelf
Title:New Trends in Applied Harmonic Analysis Sparse Representations, Compressed Sensing, and Multifractal Analysis
Author(s):
Date:2016
Size:1 online resource (19 p.)
Note:10.1007/978-3-319-27873-5
Contents:Multifractal Analysis of Cantor-like Measures -- Multifractal Analysis and Wavelets -- An Introduction to Mandelbrot Cascades -- Lebesgue-type Inequalities for Greedy Approximation -- Results on Non-linear Approximation for Wavelet Bases in Weighte d Function Spaces -- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem -- Model Sets and New Versions pf Shannon Sampling Theorem -- Stylometry and Mathematical Study of Authorship -- Thoughts on Numerical and Conceptua l Harmonic Analysis
ISBN:9783319278735
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Harmonic analysis , Fourier analysis , Measure theory , Computer science , Computer mathematics , Mathematics , Fourier Analysis , Abstract Harmonic Analysis , Signal, Image and Speech Processing , Measure and Integration , Mathematical Applications in Computer Science
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Call number:SPRINGER-2016-9783319278179:ONLINE Show nearby items on shelf
Title:Exercises in Analysis Part 2: Nonlinear Analysis
Author(s): Leszek Gasiński
Date:2016
Size:1 online resource (1062 p.)
Note:10.1007/978-3-319-27817-9
Contents:1. Function Spaces -- 2. Nonlinear and Multivalued Maps -- 3. Smooth and Nonsmooth Calculus -- 4. Degree Theory. Fixed Point Theory -- 5. Variational and Topological Methods -- Index
ISBN:9783319278179
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Functional analysis , Measure theory , Probabilities , Topology , Mathematics , Functional Analysis , Measure and Integration , Probability Theory and Stochastic Processes , Topology
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Call number:SPRINGER-2016-9781447168119:ONLINE Show nearby items on shelf
Title:Lectures on Functional Analysis and the Lebesgue Integral
Author(s): Vilmos Komornik
Date:2016
Size:1 online resource (403 p.)
Note:10.1007/978-1-4471-6811-9
Contents:Some papers of general interest -- Topological prerequisites -- Part 1 Functional analysis -- Hilbert spaces -- Banach spaces -- Locally convex spaces -- Part 2 The Lebesgue integral -- Monotone functions -- The Lebesgue integral in R -- Generalize d Newton-Leibniz formula -- Integrals on measure spaces -- Part 3 Function spaces -- Spaces of continuous functions -- Spaces of integrable functions -- Almost everywhere convergence -- Hints and solutions to some exercises -- Bibliography -- Teaching rem arks -- Subject index -- Name index
ISBN:9781447168119
Series:eBooks
Series:SpringerLink (Online service)
Series:Springer eBooks
Keywords: Mathematics , Approximation theory , Functional analysis , Measure theory , Mathematics , Functional Analysis , Measure and Integration , Approximations and Expansions
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Call number:SPRINGER-2014-9783642450822:ONLINE Show nearby items on shelf
Title:A Measure Theoretical Approach to Quantum Stochastic Processes [electronic resource]
Author(s): Wilhelm Waldenfels
Date:2014
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
Size:1 online resource
Note:This monograph takes as starting point that abstract quantum stochastic processes can be understood as a quantum field theory in one space and in one time coordinate. As a result it is appropriate to represent operators as powerseries of creation and annihilation operators in normal-ordered form, which can be achieved using classical measure theory. Considering in detail four basic examples (e.g. a two-level atom coupled to a heat bath of oscillators), ineach case the Hamiltonian of the associated o ne-parameter strongly continuous group is determined and the spectral decomposition is explicitly calculated in the form of generalized eigen-vectors. Advanced topics include the theoryof the Hudson-Parthasarathy equation and the amplified oscillator pro blem. To that end, a chapter on white noise calculus has also been included
Contents:Weyl Algebras
Continuous Sets of Creation and Annihilation Operators
One
Parameter Groups
Four Explicitly Calculable One
Excitation Processes
White Noise Calculus
Circled Integrals
White Noise Integration
The Hudson
Parthasarathy Differential Equation
The Amplifies Oscillator
Approximation by Coloured Noise
Index
ISBN:9783642450822
Series:eBooks
Series:SpringerLink
Series:Lecture Notes in Physics, 0075-8450 : v878
Series:Physics and Astronomy (Springer-11651)
Keywords: Quantum theory , Mathematical physics
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Call number:SPRINGER-2014-9783319061764:ONLINE Show nearby items on shelf
Title:Exercises in Analysis [electronic resource] : Part 1
Author(s): Leszek Gasiksi
Nikolaos S Papageorgiou
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces topological spaces measure, integration, and Martingales measure andtopology and functional analysis . Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for betterunderstanding of the material. At least 170 exercises/problems ar e presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for theapplication surrounding each topic. This nearly encyclopedic coverage of exercises in mathemat ical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problemsvaluable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all ofthe above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume
Contents:1. Metric Spaces
2. Topological Spaces
3. Measure, Integral, and Martingales
4. Measures and Topology
5. Functional Analysis
Other Problem Books
List of Symbols
Index
ISBN:9783319061764
Series:eBooks
Series:SpringerLink
Series:Problem Books in Mathematics, 0941-3502
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Distribution (Probability theory) , Topology
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Call number:SPRINGER-2014-9783319060743:ONLINE Show nearby items on shelf
Title:Functional Analysis and Applied Optimization in Banach Spaces [electronic resource] : Applications to Non-Convex Variational Models
Author(s): Fabio Botelho
Date:2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physicsand engineering probl ems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation.Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dualapproach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in relatedfields
Contents:1. Topological Vector Spaces
2. The Hahn
Bananch Theorems and Weak Topologies
3. Topics on Linear Operators
4.Basic Results on Measure and Integration
5. The Lebesgue Measure in Rn
6. Other Topics in Measure and Integration
7. Distributions
8. The Lebesque and Sobolev Spaces
9. Basic Concepts on the Calculus of Variations
10. Basic Concepts on Convex Analysis
11. Constrained Variational Analysis
12. Duality Applied to Elasticity
13. Duality Applied to a Plate Model
14. About Ginzburg
Landau Type Equations: The Simpler Real Case
15. Full Complex Ginzb
ISBN:9783319060743
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Functional analysis , Numerical analysis
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Call number:SPRINGER-2014-9783319057927:ONLINE Show nearby items on shelf
Title:Principles of Harmonic Analysis [electronic resource]
Author(s): Anton Deitmar
Siegfried Echterhoff
Date:2014
Edition:2nd ed. 2014
Publisher:Cham : Springer International Publishing : Imprint: Springer
Size:1 online resource
Note:This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respectivegeneralizations to non-abelian grou ps, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelicgroups, as well as a complementary section on direct an d projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonicanalysis and for researchers seeking to apply it
Contents:1. Haar Integration
2. Banach Algebras
3. Duality for Abelian Groups
4. The Structure of LCA
Groups
5. Operators on Hilbert Spaces
6. Representations
7. Compact Groups
8. Direct Integrals
9. The Selberg Trace Formula
10. The Heisenberg Group
11. SL2(R)
12. Wavelets
13. p
adic numbers and adeles
A. Topology
B. Measure and Integration
C: Functional Analysis
ISBN:9783319057927
Series:eBooks
Series:SpringerLink
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Harmonic analysis , Visualization
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Call number:SPRINGER-2014-9783034806947:ONLINE Show nearby items on shelf
Title:A Course on Integration Theory [electronic resource] : including more than 150 exercises with detailed answers
Author(s): Nicolas Lerner
Date:2014
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathodory Theorem. It also includes some elementary properties ofHausdorff measures as we ll as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change-of-variables formulas as well as the constructionand study of classical Cantor sets are treate d in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality, are proven. Further topics include the Radon-Nikodym theorem, notions ofharmonic analysis, classical inequalities and interpolation theore ms including Marcinkiewicz's theorem, and the definition of Lebesgue points and the Lebesgue differentiation theorem. Each chapter ends with a large number of exercisesand detailed solutions. A comprehensive appendix provides the reader with various eleme nts of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. It also provides more advancedmaterial such as some basic properties of cardinals and ordinals which are useful for the study of measurabi lity
Contents:1 Introduction
2 General theory of integration
3 Construction of the Lebesgue measure on R^d
4 Spaces of integrable functions
5 Integration on a product space
6 Diffeomorphisms of open subsets of R^d and integration
7 Convolution
8 Complex measures
9 Harmonic analysis
10 Classical inequalities
ISBN:9783034806947
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2014-9781461496380:ONLINE Show nearby items on shelf
Title:Real Analysis for the Undergraduate [electronic resource] : With an Invitation to Functional Analysis
Author(s): Matthew A Pons
Date:2014
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis.While these advanced t opics are not typically encountered until graduate study, the text is designed for the beginner. The authors engaging style makes advanced topics approachable without sacrificing rigor. The text alsoconsistently encourages the reader to pick up a pencil a nd take an active part in the learning process. Key features include: - examples to reinforce theory - thorough explanations preceding definitions, theorems and formal proofs -illustrations to support intuition - over 450 exercises designed to develop con nections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delvedeeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate cu rriculum
Contents:The Real Numbers
Sequences in R
Numerical Series
Continuity
The Derivative
Sequence and Series of Functions
The Riemann Integral
Lebesgue Measure on R
Lebesgue Integration
ISBN:9781461496380
Series:eBooks
Series:SpringerLink
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis
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Call number:SPRINGER-2014-9781461495871:ONLINE Show nearby items on shelf
Title:Introduction to Stochastic Integration [electronic resource]
Author(s): K.L Chung
R.J Williams
Date:2014
Edition:2nd ed. 2014
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduatecourse in stochastic ca lculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales then Its change of variable formula is developedfor continuous martingales. Applications include a c haracterization of Brownian motion, Hermite polynomials of martingales, the FeynmanKac functional and theSchrdinger equation. For Brownian motion, the topics of local time,reflected Brownian motion, and time change are discussed. New to the second editio n are a discussion of the CameronMartinGirsanov transformation and a final chapter which provides an introduction to stochastic differentialequations, as well as many exercises for classroom use. This book will be a valuable resource to all mathematician s, statisticians, economists, and engineers employing the modern tools of stochastic analysis. The text also provesthat stochastic integration has made an important impact on mathematical progress over the last decades and that stochastic calculus has be come one of the most powerful tools in modern probability theory. Journal of the AmericanStatistical Association An attractive textwritten in [a] lean and precise styleeminently readable. Especially pleasant are the care and attention devoted to details A very fine book. Mathematical Reviews
Contents:1 Preliminaries
2 Definition of the Stochastic Integral
3 Extension of the Predictable Integrands
4 Quadratic Variation Process
5 The Ito Formula
6 Applications of the Ito Formula
7 Local Time and Tanaka's Formula
8 Reflected Brownian Motions
9 Generalization Ito Formula, Change of Time and Measure
10 Stochastic Differential Equations
References
Index
ISBN:9781461495871
Series:eBooks
Series:SpringerLink
Series:Modern Birkhuser Classics, 2197-1803
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2014-9780817684099:ONLINE Show nearby items on shelf
Title:A Probability Path [electronic resource]
Author(s): Sidney I Resnick
Date:2014
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Many probability books are written by mathematicians and have the built-in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate studentsfrom a variety of disci plines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research instatistics, applied probability, biology, operations research, mathematical finance, and engineering. Aone-semester course is laid out in an efficient and readable manner covering the core material. The first three chaptersprovide a functioning knowledge of measure theory. Chapter 4 discusses independence, with expectation and integration covered in Chapter 5, followed by topics on different modes of convergence, laws of large numbers with applicationsto statistics (quantile and distribution function estimation), and applied probability. Two subsequent cha pters offer a careful treatment of convergence in distribution and the central limit theorem. The final chapter treatsconditional expectation and martingales, closing with a discussion of two fundamental theorems of mathematical finance. Like Adventures in Stochastic Processes, Resnicks related and very successful textbook, A Probability Path isrich in appropriate examples, illustrations, and problems, and is suitable for classroom use or self-study. The present uncorrected, softcover reprintis designed to make this classic textbookavailable to a wider audience. This book is different from the classical textbooks on probability theory in that it treats the measure theoreticbackground not as a prerequisite but as an integral part of probability theory. Th e result is that the reader gets a thorough and well-structured framewo
ISBN:9780817684099
Series:eBooks
Series:SpringerLink
Series:Modern Birkhuser Classics, 2197-1803
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory) , Mathematical statistics
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Call number:SPRINGER-2013-9783034806367:ONLINE Show nearby items on shelf
Title:Introduction to Mathematical Analysis [electronic resource]
Author(s): Igor Kriz
Ale Pultr
Date:2013
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, theLebesgue integral, vector calculus anddifferential equations. Af ter having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differentialgeometry and even functional analysis. Overall, this t ext provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today
Note:Springer eBooks
Contents:Preface
Introduction
Part 1. A Rigorous Approach to Advanced Calculus
1. Preliminaries
2. Metric and Topological Spaces I
3. Multivariable Differential Calculus
4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral
5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration
6. Systems of Ordinary Differential Equations
7. System of Linear Differential Equations
8. Line Integrals and Green's Theorem
Part 2. Analysis and Geometry
9. An Introduction to Complex Analysis
10. Metric and Top
ISBN:9783034806367
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Matrix theory , Functions of complex variables , Differential Equations , Sequences (Mathematics)
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Call number:SPRINGER-2013-9781461480242:ONLINE Show nearby items on shelf
Title:Lie Groups [electronic resource]
Author(s): Daniel Bump
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
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Note:Springer 2013 e-book collections
Note:This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range ofmaterial to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests.This second edition has substantial new material, including improved discussions ofunderlying principles, streamlining of some pro ofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the PeterWeyl theorem, Lie algebra, conjugacy of maximal tori, the Weylgroup, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flagvarieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics tha t are treated are symmetric function theory, the representation theory of the symmetric group, FrobeniusSchur duality andGL(n)GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatoric s of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and thecohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations
Note:Springer eBooks
Contents:Part I: Compact Topological Groups
1 Haar Measure
2 Schur Orthogonality
3 Compact Operators
4 The PeterWeyl Theorem
Part II: Compact Lie Groups
5 Lie Subgroups of GL(n,C)
6 Vector Fields
7 Left
Invariant Vector Fields
8 The Exponential Map
9 Tensors and Universal Properties
10 The Universal Enveloping Algebra
11 Extension of Scalars
12 Representations of sl(2,C)
13 The Universal Cover
14 The Local Frobenius Theorem
15 Tori
16 Geodesics and Maximal Tori
17 The Weyl Integration Formula
18 The Root System
19 Examples of Root Systems
ISBN:9781461480242
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v225
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups
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Call number:SPRINGER-2013-9781461471967:ONLINE Show nearby items on shelf
Title:Measure, Integral, Derivative [electronic resource] : A Course on Lebesgue's Theory
Author(s): Sergei Ovchinnikov
Date:2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This classroom-tested text is intended for a one-semester course in Lebesgues theory. With over 180 exercises, the texttakes an elementary approach, making iteasily accessible toboth upper-undergraduate- andlower-graduate-level students. The three ma in topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, anintroductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiabilityproperty of functions of bounded variations, are dissected into small steps in order to be accessi ble to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary,where -algebras are not used in the text on measure theory and Dinis derivatives are not used in the chapter on differentiat ion. However, all the main results of Lebesgues theory are found in the book
Note:Springer eBooks
Contents:1 Preliminaries
2 Lebesgue Measure
3 Lebesgue Integration
4 Differentiation and Integration
A Measure and Integral over Unbounded Sets
Index
ISBN:9781461471967
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2013-9781461469568:ONLINE Show nearby items on shelf
Title:Measure Theory [electronic resource] : Second Edition
Author(s): Donald L Cohn
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Intended as a self-contained introduction to measure theory, this textbook also includesa comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haarmeasures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and theexistence of liftings. Measure Theory provides a soli d background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. Theprerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review ofessential background material. The author aims to present a straightforward treatment of thepart of measure theory necessary for analysis and probability' assuming only basic knowledge of analysis and topol ogy...Each chapter includes numerous well-chosen exercises, varying from very routine practice problems to importantextensions and developments of the theory for the difficult ones there are helpful hints. It is the reviewer's opinion that the author has succeeded in his aim. In spite of its lack of new results, the selection and presentation ofmaterials makes this a useful book for an introduction to measure and integration theory. Mathematical Reviews (Review of the First Edition) The book is a compreh ensive and clearly written textbook on measure andintegration...The book contains appendices on set theory, algebra, calculus and topology in Euclidean spaces, topological and metric spaces, and the Bochner integral. Each section of the book contains a nu mber of exercises.zbMATH (Review of the First Edition)
Note:Springer eBooks
Contents:1. Measures
Algebras and sigma
algebras
Measures
Outer measures
Lebesgue measure
Completeness and regularity
Dynkin classes
2. Functions and Integrals
Measurable functions
Properties that hold almost everywhere
The integral
Limit theorems
The Riemann integral
Measurable functions again, complex
valued functions, and image measures
3. Convergence
Modes of Convergence
Normed spaces
Definition of L^p and L^p
Properties of L^p and L
p
Dual spaces
4. Signed and Complex Measures
Signed and complex measures
Absolute continuity
Singu
ISBN:9781461469568
Series:e-books
Series:SpringerLink (Online service)
Series:Birkhuser Advanced Texts Basler Lehrbcher, 1019-6242
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Distribution (Probability theory)
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Call number:SPRINGER-2013-9781461459620:ONLINE Show nearby items on shelf
Title:Foundations of Abstract Analysis [electronic resource]
Author(s): Jewgeni H Dshalalow
Date:2013
Edition:2nd ed. 2013
Publisher:New York, NY : Springer New York : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presentedin a self-contained wa y suitable both for classroom use and for self-study. While this book carries the rigor of advancedmodern analysis texts, it elaborates the material in much greater details and therefore fills a gap betweenintroductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of thepotential overload of new words, definitions, and concepts, the book (in its u nique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded byinformal discussions and blueprints followed by thorough details andsupported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of thebook, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. P rerequisites include advanced calculus, linear algebra, complex variables, and calculus basedprobability
Note:Springer eBooks
Contents:Set
Theoretic and Algebraic Preliminaries
Analysis of Metric Spaces
Elements of Point
Set Topology
Measurable Spaces and Measurable Functions
Measures
Integration in Abstract Spaces
Solutions to Selected Problems
Bibliography
List of Symbols
Index of Names and Terms
ISBN:9781461459620
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Numerical analysis
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Call number:SPRINGER-2013-9781461452577:ONLINE Show nearby items on shelf
Title:Real and Convex Analysis [electronic resource]
Author(s): Erhan nlar
Robert J Vanderbei
Date:2013
Publisher:Boston, MA : Springer US : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This book offers a first course in analysis for scientists and engineers. It can be used at the advanced undergraduate level or as part of the curriculum in a graduate program. The book is built around metric spaces. Inthe first three chapters, the authors lay the foundational material and cover the all-important four-Cs: convergence, completeness, compactness, and continuity.In subsequent chapters, the basic tools of analysis are used togive brief introductions to differential and integralequations , convex analysis, and measure theory. The treatment is modern and aesthetically pleasing. The book contains detailed illustrations, examples and exercises. It laysthe groundwork for the needs of classical fields as well as the important new fields of op timization and probability theory
Note:Springer eBooks
Contents:Sets and Functions
Metric Spaces
Functions on Metric Spaces
Differential and Integral Equations
Convexity
Convex Optimization
Measure and Integration
Bibiography
Index
ISBN:9781461452577
Series:e-books
Series:SpringerLink (Online service)
Series:Undergraduate Texts in Mathematics, 0172-6056
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Mathematical optimization , Engineering mathematics
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Call number:SPRINGER-2013-9781447151227:ONLINE Show nearby items on shelf
Title:Real Analysis: Measures, Integrals and Applications [electronic resource]
Author(s): Boris Makarov
Anatolii Podkorytov
Date:2013
Publisher:London : Springer London : Imprint: Springer
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications bothclassical and those rarely co vered in literature. This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines theconcept of the Hausdorff measure, the properties of the a rea on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied toharmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables. The book contains more than 600 examples andexercises. The reader who has mastered the first third of the book will be able to study other areas of mat hematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory,statistics, functional analysis, partial differential equations and others. Real Analysis: Measures, Integrals and Applications is inte nded for advanced undergraduate and graduate students in mathematics and physics. It assumes thatthe reader is familiar with basic linear algebra and differential calculus of functions of several variables
Note:Springer eBooks
Contents:Measure
The Lebesgue Model
Measurable Functions
The Integral
The Product Measure
Change of Variables in an Integral
Integrals Dependent on a Parameter
Surface Integrals
Approximation and Convolution of the Space
Fourier Series and the Fourier Transform
Charges. The Radon
Nikodym Theory
Integral Representation of Linear Functionals
Appendices
ISBN:9781447151227
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Geometry
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Call number:SPRINGER-2012-9783034803823:ONLINE Show nearby items on shelf
Title:Measure and Integration [electronic resource] : Publications 1997-2011
Author(s): Heinz Knig
Date:2012
Publisher:Basel : Springer Basel : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This volume presents a collection of twenty-five of Heinz Knigs recent and most influential works. Connecting to his book of 1997 Measure and Integration, the author has developed a consistent new version of measuretheory over the past years. For the first time, his publications are collected here in one single volume. Key features include: - A first-time, original and entirely uniform treatment of abstract and topological measure theory - Theintroduction of the inner and outer premeasures and thei r extension to unique maximal measures - A simplification of the procedure formerly described in Chapter II of the authors previous book - The creation of newenvelopes for the initial set function (to replace the traditional Carathodory outer measures), w hich lead to much simpler and more explicit treatment - The formation of products, a unified Daniell-Stone-Riesz representationtheorem, and projective limits, which allows to obtain the Kolmogorov type projective limit theorem for even huge domains far be yond the countably determined ones - The incorporation of non-sequential and of inner regular versions,which leads to much more comprehensive results - Significant applications to stochastic processes. Measure and Integration: Publications 19972011 will a ppeal to both researchers and advanced graduate students in the fields ofmeasure and integration and probabilistic measure theory
Note:Springer eBooks
Contents:Image measures and the so
called image measure catastrophe
The product theory for inner premeasures
Measure and Integration: Mutual generation of outer and inner premeasures
Measure and Integration: Integral representations of isotone functionals
Measure and Integration: Comparison of old and new procedures
What are signed contents and measures?
Upper envelopes of inner premeasures
On the inner Daniell
Stone and Riesz representation theorems
Sublinear functionals and conical measures
Measure and Integration: An attempt at unified systematization
New facts around the
ISBN:9783034803823
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2012-9780817683467:ONLINE Show nearby items on shelf
Title:An Introduction to Continuous-Time Stochastic Processes [electronic resource] Theory, Models, and Applications to Finance, Biology, and Medicine
Author(s): Vincenzo Capasso
David Bakstein
Date:2012
Edition:2nd ed. 2012
Publisher:Boston, MA : Birkhuser Boston : Imprint: Birkhuser
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:From reviewsof First Edition: The book is... an account of fundamental concepts as they appear in relevant modern applications and literature.... The book addresses three main groups: first, mathematicians working in adifferent field second, other sc ientists and professionals from a business or academic background third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications.Zentralblatt MATH This is an introductory text on continuous ti me stochastic processes and their applications to finance and biology. ... The book will be useful for applied mathematicians who are not probabilists to get a quickflavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications. Mathematical Reviews Revised and enhanced, this conciselywritten second edition of An Introduction toContinuous-Time Stochastic Processes is a rigorousand self-contained introduction to the theoryof continuous-time st ochastic processes, stochastic integrals,and stochastic differentialequations. Expertly balancing theory andapplications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and ins urance using stochastic methods. No previous knowledge of stochastic processes isrequired. Key topicsinclude: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics * Agent-based models New to the Second Edition: * Improvedpresentation of original concepts * Expanded background on probability theory * Substantial material applicable tofinance and biology, including stable laws, Lvy processes, and It-Lvy calculus *Sup plemental appendix toprovidebasic facts on semigroups of linear operators An Introduction to Continuous-Time Stochastic Processes, Second Editionwill be of inte
Note:Springer eBooks
Contents:Part I. The Theory of Stochastic Processes
Fundamentals of Probability
Stochastic Processes
The It Integral
Stochastic Differential Equations
Part II. The Applications of Stochastic Processes
Applications to Finance and Insurance
Applications to Biology and Medicine
Part III. Appendices
Measure and Integration
Convergence of Probability Measures on Metric Spaces
Elliptic and Parabolic Operators
D Semigroups and Linear Operators
E Stability of Ordinary Differential Equations
References
ISBN:9780817683467
Series:e-books
Series:SpringerLink (Online service)
Series:Modeling and Simulation in Science, Engineering and Technology, 2164-3679
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Finance , Distribution (Probability theory) , Engineering mathematics
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Call number:SPRINGER-2012-9780817683108:ONLINE Show nearby items on shelf
Title:Mathematical Analysis [electronic resource] : Foundations and Advanced Techniques for Functions of Several Variables
Author(s): Mariano Giaquinta
Giuseppe Modica
Date:2012
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in anearlier introductory v olume. The presentation is largely focused on the foundations of measure and integration theory. The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differentialforms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics.The authorsconclude with the study of measure and integration theory Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. Thiswork may be used as a supplementary text in the classroom or for self-study by advanced undergra duate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengthsof this presentation, along with the other four books on analysis published by the authors, is the motivation for und erstanding the subject through examples, observations, exercises, and illustrations. Other books published by theauthors all of which provide the reader with a strong foundation in modern-day analysis include: * Mathematical Analysis: Functions of One V ariable * Mathematical Analysis: Approximation and Discrete Processes * MathematicalAnalysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematica l Analysis: The presentation of the theory is clearly arranged,all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requ
Note:Springer eBooks
Contents:Preface
Spaces of Summable Functions and Partial Differential Equations
Convex Sets and Convex Functions
The Formalism of the Calculus of Variations
Differential Forms
Measures and Integrations
Hausdorff and Radon Measures
Mathematicians and Other Scientists
Bibliographical Notes
Index
ISBN:9780817683108
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2011-9788876423864:ONLINE Show nearby items on shelf
Title:Introduction to Measure Theory and Integration [electronic resource]
Author(s): Luigi Ambrosio
Giuseppe Prato
Andrea Mennucci
Date:2011
Publisher:Pisa : Edizioni della Normale
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook collects the notes for an introductory course in measure theory and integration. The course was taught by the authors to undergraduate students of the Scuola Normale Superiore, in the years 2000-2011. The goal of thecourse was to presen t, in a quick but rigorous way, the modern point of view on measure theory and integration, putting Lebesgue's Euclidean space theory into a more general context and presenting the basic applications to Fourierseries, calculus and real analysis. The text can also pave the way to more advanced courses in probability, stochastic processes or geometric measure theory. Prerequisites for the book are a basic knowledge of calculus in one andseveral variables, metric spaces and linear algebra. All results presen ted here, as well as their proofs, are classical. The authors claim some originality only in the presentation and in the choice of the exercises. Detailed solutionsto the exercises are provided in the final part of the book
Note:Springer eBooks
Contents:Measure spaces
Integration
Spaces of measurable functions
Hilbert spaces
Fourier series
Operations on measures
The fundamental theorem of integral calculus
Operations on measures
Appendix: Riesz representation theorem of the dual of C(K) and integrals depending on a parameter
Solutions to the exercises
ISBN:9788876423864
Series:e-books
Series:SpringerLink (Online service)
Series:Appunti/Lecture Notes : v10
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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Call number:SPRINGER-2011-9781461411352:ONLINE Show nearby items on shelf
Title:Essentials of Integration Theory for Analysis [electronic resource]
Author(s): Daniel W Stroock
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:Essentials of Integration Theory for Analysis is a substantial revision of the best-selling Birkhuser title by the same author, A Concise Introduction to the Theory of Integration. Highlights of this new textbook for the GTMseries include revisions t o Chapter 1 which add a section about the rate of convergence of Riemann sums and introduces a discussion of the EulerMacLauren formula. In Chapter 2, where Lebesques theory is introduced, aconstruction of the countably additive measure is done with suffi cient generality to cover both Lebesque and Bernoulli measures. Chapter 3 includes a proof of Lebesques differential theorem for all monotone functions and theconcluding chapter has been expanded to include a proof of Carathorys method for constructing me asures and his result is applied to the construction of the Hausdorff measures. This new gem is appropriate as a text for aone-semester graduate course in integration theory and is complimented by the addition of several problems related to the new materi al. The text is also highly useful for self-study. A complete solutions manual is available forinstructors who adopt the text for their courses. Additional publications by Daniel W. Stroock: An Introduction to Markov Processes, 2005 Springer (GTM 230), IS BN: 978-3-540-23499-9 A Concise Introduction to the Theory ofIntegration, 1998 Birkhuser Boston, ISBN: 978-0-8176-4073-6 (with S.R.S. Varadhan) Multidimensional Diffusion Processes, 1979 Springer (Classics in Mathematics), ISBN: 978-3-540-28998-2
Note:Springer eBooks
ISBN:9781461411352
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v262
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics)
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Call number:SPRINGER-2011-9781441969507:ONLINE Show nearby items on shelf
Title:Concrete Functional Calculus [electronic resource]
Author(s): R. M Dudley
R Norvaia
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- oroperator-valued coefficient f unction into a solution of a system of linear differential equations with the given coefficients. For nonlinear integral equations with respect to possibly discontinuous functions having unboundedvariation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * Applications to stochastic processes. This work will serve as a thoroughreference on its main topics for researchers and graduate students with a backgro und in real analysis and, for Chapter 12, in probability
Note:Springer eBooks
Contents:Preface
1 Introduction and Overview
2 Definitions and Basic Properties of Extended Riemann
Stieltjes Integrals
3 Phi
variation and p
variation Inequalities for Integrals
4 Banach Algebras
5 Derivatives and Analyticity in Normed Spaces
6 Nemytskii Operators on Some Function Spaces
7 Nemytskii Oerators on Lp Spaces
8 Two
Function Composition
9 Product Integration
10 Nonlinear Differential and Integral Equations
11 Fourier Series
12 Stochastic Processes and Phi
Variation
Appendix Nonatomic Measure Spaces
References
Subject Index
Author Index
Ind
ISBN:9781441969507
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Monographs in Mathematics, 1439-7382
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Integral equations , Operator theory
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Call number:SPRINGER-2011-9780817647919:ONLINE Show nearby items on shelf
Title:A Modern Approach to Functional Integration [electronic resource]
Author(s): John R Klauder
Date:2011
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
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Note:This text takes advantage of recent developments in the theory of path integration to provide an improved treatment of quantization of systems that either have no constraints or instead involve constraints with demonstrativelyimproved procedures. Str ong emphasis is placed on the coherent state form of the path integral, which typically is only briefly mentioned in the textbook literature. Also of prime importance, a key focus of the book will be on theprojection operator method of enforcing quantum c onstraints. Additionally, several novel proposals are introduced to deal with highly singular quantum field theories. The modern treatment used by the author is an attempt to make amajor paradigm shift in how the art of functional integration is practiced . The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and appliedmathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. Ke y topics and features: * A thorough grounding in the Gold Standard of path integrals: the Wiener measure * Formulation of all pathintegral construction from abstract principles * A review of coherent state fundamentals * A critical comparison of several p ath integral versions with emphasis on the virtues of the coherent state version * A construction of theWiener-measure regularized phase space path integral, its emergence as a coherent state path integral, and its superior definition and connection to th e classical theory underlying the quantization * A review of classical and quantumconstraints and some of their traditional treatments * Introduction of the projection operator method to deal with quantum constraints, its many virtues as compared to tradi tional methods, and how it can be incorporated into aconventional or coherent state phase space path integral * An extension of the books principal discussion into the realm of quantum field theory w
Note:Springer eBooks
Contents:Preface
Introduction
Part I: Stochastic Theory
Probability
Infinite
Dimensional Integrals
Stochastic Variable Theory
Part II: Quantum Theory
Background to an Analysis of Quantum Mechanics
Quantum Mechanical Path Integrals
Coherent State Path Integrals
Continuous
Time Regularized Path Integrals
Classical and Quantum Constraints
Part III: Quantum Field Theory
Application to Quantum Field Theory
A Modern Approach to Nonrenormalizable Models
References
Index
ISBN:9780817647919
Series:e-books
Series:SpringerLink (Online service)
Series:Applied and Numerical Harmonic Analysis
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Functional analysis , Differential equations, partial , Quantum theory
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Call number:SPRINGER-2011-9780387878591:ONLINE Show nearby items on shelf
Title:Probability and Stochastics [electronic resource]
Author(s): Erhan inlar
Date:2011
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In manyinstances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces,conditional expectations, and the classical limit theo rems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures andtheir roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The bookis based on the authors lecture notes incourses offered over the years at Princeton University. These courses attracted graduate students from enginee ring, economics, physics, computer sciences, and mathematics. Erhan inlar has received many awards for excellence inteaching, including the Presidents Award for Distinguished Teaching at Princeton University. His research interests include theories of Ma rkov processes, point processes, stochastic calculus, and stochastic flows. The book is fullof insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style
Note:Springer eBooks
Contents:Preface
Measure and Integration
Probability Spaces
Convergence
Conditioning
Martingales and Stochastics
Poisson Random Measures
Levy Processes
Index
Bibliography
ISBN:9780387878591
Series:e-books
Series:SpringerLink (Online service)
Series:Graduate Texts in Mathematics, 0072-5285 : v261
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2010-9783834896391:ONLINE Show nearby items on shelf
Title:The CMS Silicon Strip Tracker [electronic resource] Concept, Production, and Commissioning
Author(s): Oliver Pooth
Date:2010
Publisher:Wiesbaden : Vieweg+Teubner
Size:1 online resource
Note:Springer e-book platform
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Note:With the start of the Large Hadron Collider LHC at CERN near Geneva, Switzerland, and the huge detectors along this particle accelerator, the largest high energy physics experiments ever are underway. One of the experiments is theCMS detector (Compac t Muon Solenoid). With this experiment over 3,000 scientists and engineers worldwide will search for answers to fundamental questions in high energy physics. Oliver Pooth describes the silicon strip tracker of theCMS detector. With a sensitive silicon are a of 200 m it is a central part of the experiment and able to precisely measure charged particles originating from high energy proton collisions at the LHC. In total, more than 15,000individual silicon strip detector modules were built and tested before t hey were integrated on larger substructures of the silicon strip tracker. The author discusses methods of quality control that are new to the field of particledetector physics. These methods were established to guarantee a uniform behaviour of all detecto r modules which were built and tested in various places worldwide. After integration into the CMS experiment and commissioning, the siliconstrip tracker is now ready to operate for at least ten years of LHC running
Note:Springer eBooks
ISBN:9783834896391
Series:e-books
Series:SpringerLink (Online service)
Series:Physics and Astronomy (Springer-11651)
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Call number:SPRINGER-2010-9783764385149:ONLINE Show nearby items on shelf
Title:Pseudo-Differential Operators and Symmetries [electronic resource] : Background Analysis and Advanced Topics
Author(s): Michael Ruzhansky
Ville Turunen
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:This monograph develops a global quantization theory of pseudo-differential operators on compact Lie groups. Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim oftackling a number of import ant problems in analysis and in the theory of partial differential equations. This also yields a local theory of pseudo-differential operators on manifolds. The present book takes a different approach byusing global symmetries of the space which are often available. First, a particular attention is paid to the theory of periodic operators, which are realized in the form of pseudo-differential and Fourier integral operators on thetorus. Then, the cases of the unitary group SU(2) and the 3-sphere are analyz ed in extensive detail. Finally, the monograph also develops elements of the theory of pseudo-differential operators on general compact Lie groups andhomogeneous spaces. The exposition of the book is self-contained and provides the reader with the backgro und material surrounding the theory and needed for working with pseudo-differential operators in different settings. Thebackground section of the book may be used for independent learning of different aspects of analysis and is complemented by numerous ex amples and exercises
Note:Springer eBooks
Contents:Preface
Introduction
Part I Foundations of Analysis
A Sets, Topology and Metrics
B Elementary Functional Analysis
C Measure Theory and Integration
D Algebras
Part II Commutative Symmetries
1 Fourier Analysis on Rn
2 Pseudo
differential Operators on Rn
3 Periodic and Discrete Analysis
4 Pseudo
differential Operators on Tn
5 Commutator Characterisation of Pseudo
differential Operators
Part III Representation Theory of Compact Groups
6 Groups
7 Topological Groups
8 Linear Lie Groups
9 Hopf Algebras
Part IV Non
commutative Symmetries
10 Pseu
ISBN:9783764385149
Series:e-books
Series:SpringerLink (Online service)
Series:Pseudo-Differential Operators, Theory and Applications : v2
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Topological Groups , Global analysis , Differential equations, partial
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Call number:SPRINGER-2010-9783540328278:ONLINE Show nearby items on shelf
Title:Handbook of Partial Least Squares [electronic resource] : Concepts, Methods and Applications
Author(s): Vincenzo Esposito Vinzi
Wynne W Chin
Jrg Henseler
Huiwen Wang
Date:2010
Publisher:Berlin, Heidelberg : Springer Berlin Heidelberg
Size:1 online resource
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Note:The Handbook of Partial Least Squares (PLS) and Marketing: Concepts, Methods and Applications is the second volume in the series of the Handbooks of Computational Statistics. This Handbook represents a comprehensive overviewof PLS methods with specif ic reference to their use in Marketing and with a discussion of the directions of current research and perspectives. The Handbook covers the broad area of PLS Methods from Regression to Structural EquationModeling, from methods to applications, from softw are to interpretation of results. The Handbook features papers on the use and the analysis of latent variables and indicators by means of the PLS Path Modeling approach from the designof the causal network to the model assessment and improvement. Moreover , within the PLS framework, the Handbook addresses, among others, special and advanced topics such as the analysis of multi-block, multi-group and multi-structureddata, the use of categorical indicators, the study of interaction effects, the integration o f classification issues, the validation aspects and the comparison between thecomponent-basedPLS approach and the covariance-basedStructural Equation Modeling. Most chapters comprise a thorough discussion of applications to problems from Marketing and rel ated areas. Furthermore, a few tutorials focus on some key aspects of PLS analysis with a didactic approach.This Handbook serves as both an introduction for those without prior knowledge of PLS as well as a comprehensive reference for researchers and prac titioners interested in the most recent advances in PLS methodology
Note:Springer eBooks
Contents:Editorial: Perspectives on Partial Least Squares
METHODS
Latent Variables and Indices: Herman Wolds Basic Design and Partial Least Squares
PLS Path Modeling: From Foundations to Recent Developments and Open Issues for Model Assessment and Improvement
Bootstrap Cross
Validation Indices for PLS Path Model Assessment
A Bridge Between PLS Path Modeling and Multi
Block Data Analysis
Use of ULS
SEM and PLS
SEM to Measure a Group Effect in a Regression Model Relating Two Blocks of Binary Variables
A New Multiblock PLS Based Method to Estimate Causal Models: Application to the
ISBN:9783540328278
Series:e-books
Series:SpringerLink (Online service)
Series:Springer Handbooks of Computational Statistics
Series:Mathematics and Statistics (Springer-11649)
Keywords: Statistics , Mathematical statistics , Marketing
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Call number:SPRINGER-2010-9783034602112:ONLINE Show nearby items on shelf
Title:Vector Measures, Integration and Related Topics [electronic resource]
Author(s): Guillermo P Curbera
Gerd Mockenhaupt
Werner J Ricker
Date:2010
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:This volume contains a selection of articles on the theme vector measures, integration and applications together with some related topics. The articles consist of both survey style and original research papers, are written byexperts in the area and p resent a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical andharmonic analysis, operator theory, non-commutativ e integration, and functional analysis. The material is of interest to experts, young researchers and postgraduate students
Note:Springer eBooks
ISBN:9783034602112
Series:e-books
Series:SpringerLink (Online service)
Series:Operator Theory: Advances and Applications : v201
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Operator theory
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Call number:SPRINGER-2010-9781441916051:ONLINE Show nearby items on shelf
Title:Theory and Applications of Stochastic Processes [electronic resource] : An Analytical Approach
Author(s): Zeev Schuss
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences. Its aim is to make probability theory readily accessible to scientists trained in the traditional methods ofapplied mathematics, s uch as integral, ordinary, and partial differential equations and in asymptotic methods, rather than in probability and measure theory. It shows how to derive explicit expressions for quantities of interest bysolving equations. Emphasis is put on rational modeling and approximation methods. The book includes many detailed illustrations, applications, examples and exercises. It will appeal to graduate students and researchers in mathematics,physics and engineering
Note:Springer eBooks
Contents:Introduction
The Physical Brownian Motion: Diffusion and Noise
The Probability Space of Brownian Motion
Ito Integration and Calculus
Stochastic Differential Equations
The Discrete Approach and Boundary Behavior
The First Passage Time of Diffusions
Markov Processes and Diffusion Approximations
Diffusion Approximations to Langevin's Equation
Large Deviations of Markovian Jump Processes
Noise
Induced Escape from an Attractor
Stochastic Stability
Bibliography
ISBN:9781441916051
Series:e-books
Series:SpringerLink (Online service)
Series:Applied Mathematical Sciences, 0066-5452 : v170
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory) , Engineering mathematics
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Call number:SPRINGER-2010-9780817646752:ONLINE Show nearby items on shelf
Title:Distributions [electronic resource] : Theory and Applications
Author(s): J.J Duistermaat
J.A.C Kolk
Date:2010
Edition:1
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
Note:Springer 2013 e-book collections
Note:This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differentialequations and Fourier a nalysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series,and integrals that cannot be mathematically justified within the classical framework. Key features: Many examples, exercises, hints, and solutions guide the reader throughout the text. Includes an introduction to distributions,differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. TheFourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem , which in turn is used to efficiently derive numerous important results. The systematic use of pullback and pushforward introducesconcise notation. Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are inv ariant under the actions of various groups of transformations. Distributions: Theory and Applications isaimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome intr oduction to the subject, requiring only a minimal mathematical background. The workmay also serve as an excellent self-study guide for researchers who use distributions in various fields
Note:Springer eBooks
Contents:Preface
Motivation
Test Functions
Distributions
Differentiation of Distributions
Convergence of Distributions
Taylor Expansion in Several Variables
Localization
Distributions with Compact Support
Multiplication by Functions
Transposition, Pullback and Push forward
Convolution of Distributions
Fundamental Solutions
Fractional Integration and Differentiation
Fourier Transformation
Fourier Series
Fundamental Solutions and Fourier Transformation
Supports and Fourier Transformation
Sobolev Spaces
Appendix: Results from Measure Theory in the C
ISBN:9780817646752
Series:e-books
Series:SpringerLink (Online service)
Series:Cornerstones
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Fourier analysis , Differential Equations , Differential equations, partial
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Call number:SPRINGER-2010-9780387894881:ONLINE Show nearby items on shelf
Title:Stochastic Partial Differential Equations [electronic resource] : A Modeling, White Noise Functional Approach
Author(s): Helge Holden
Bernt ksendal
Jan Ube
Tusheng Zhang
Date:2010
Publisher:New York, NY : Springer New York
Size:1 online resource
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Note:The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs driven by space-time Brownian motion noise. In this, the second edition, theauthors extend the the ory to include SPDEs driven by space-time Lvy process noise, and introduce new applications of the field. Because the authors allow the noise to be in both space and time, the solutions to SPDEs are usually ofthe distribution type, rather than a classical random field. To make this study rigorous and as general as possible, the discussion of SPDEs is therefore placed in the context of Hida white noise theory. The key connection betweenwhite noise theory and SPDEs is that integration with respect to Browni an random fields can be expressed as integration with respect to the Lebesgue measure of the Wick product of the integrand with Brownian white noise, and similarlywith Lvy processes. The first part of the book deals with the classical Brownian motion case . The second extends it to the Lvy white noise case. For SPDEs of the Wick type, a general solution method is given by means of the Hermitetransform, which turns a given SPDE into a parameterized family of deterministic PDEs. Applications of this theory a re emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as areapplications to finance. Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering will find this introduction indispensible. Useful exercises are collected at the end of each chapter.From the reviews of the first edition: The authors have made significant contributions to each of the areas. As a whole, the book is well organized and very carefully w ritten and the details of the proofs are basically spelled out...This is a rich and demanding book It will be of great value for students of probability theory or SPDEs with an interest in the
Note:Springer eBooks
Contents:Preface to the Second Edition
Preface to the First Edition
Introduction
Framework
Applications to stochastic ordinary differential equations
Stochastic partial differential equations driven by Brownian white noise
Stochastic partial differential equations driven by Lvy white noise
Appendix A. The Bochner
Minlos theorem
Appendix B. Stochastic calculus based on Brownian motion
Appendix C. Properties of Hermite polynomials
Appendix D. Independence of bases in Wick products
Appendix E. Stochastic calculus based on Lvy processes
References
List of frequently
ISBN:9780387894881
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential Equations , Differential equations, partial , Distribution (Probability theory)
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Call number:SPRINGER-2009-9783764374808:ONLINE Show nearby items on shelf
Title:Analysis III [electronic resource]
Author(s): Herbert Amann
Joachim Escher
Date:2009
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:The third and last volume of this work is devoted to integration theory and the fundamentals of global analysis. Once again, emphasis is laid on a modern and clear organization, leading to a well structured and elegant theory andproviding the reader with effective means for further development. Thus, for instance, the Bochner-Lebesgue integral is considered with care, since it constitutes an indispensable tool in the modern theory of partial differentialequations. Similarly, there is discussion and a proof of a version of Stokes Theorem that makes ample allowance for the practical needs of mathematicians and theoretical physicists. As in earlier volumes, there are many glimpses ofmore advanced topics, which serve to give the reader an idea of the imp ortance and power of the theory. These prospective sections also help drill in and clarify the material presented. Numerous examples, concrete calculations, avariety of exercises and a generous number of illustrations make this textbook a reliable guide a nd companion for the study of analysis
Note:Springer eBooks
Contents:Preface
IX. Elements of Measure Theory
X. Theory of Integration
XI. Manifolds and Differential Forms
XII. Integration on Manifolds
Bibliography
Index
ISBN:9783764374808
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Global analysis
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Call number:SPRINGER-2009-9780817646561:ONLINE Show nearby items on shelf
Title:Integration and Modern Analysis [electronic resource]
Author(s): John J Benedetto
Wojciech Czaja
Date:2009
Publisher:Boston : Birkhuser Boston
Size:1 online resource
Note:Springer e-book platform
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Note:A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolutecontinuity on different iation and integration. This leads to fundamental results such as the DieudonnGrothendieck theorem and other intricate developments dealing with weak convergence of measures. Key Features: * Fascinatinghistorical commentary interwoven into the exposition * Hundreds of problems from routine to challenging * Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent studyprojects * Two significant appendices on functional analysis and Fourier analysis. K ey Topics: * In-depth development of measure theory and Lebesgue integration * Comprehensive treatment of connection between differentiation andintegration, as well as complete proofs of state-of-the-art results * Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals * Evolution of the Rieszrepresentation theorem to Radon measures and distribution theory * Deep results in modern differentiation theory * Systematic developme nt of weak sequential convergence inspired by theorems of Vitali, Nikodym, and HahnSaks *Thorough treatment of rearrangements and maximal functions * The relation between surface measure and Hausforff measure * Complete presentation of Besicovich covering s and differentiation of measures. Integration and Modern Analysiswill serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study
Note:Springer eBooks
Contents:Preface
Classical real variables
Lebesgue measure and general measure theory
The Lebesgue integral
The relationship between differentiation and integration on R
Spaces of measures and the RadonNikodym theorem
Weak convergence of measures
Riesz representation theorem
Lebesgue differentiation theorem on Rd
Self
similar sets and fractals
Appendix I: Functional analysis
Appendix II: Fourier Analysis
References
Index
ISBN:9780817646561
Series:e-books
Series:SpringerLink (Online service)
Series:Birkhuser Advanced Texts / Basler Lehrbcher
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Global analysis (Mathematics) , Functions of complex variables
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Call number:SPRINGER-2009-9780387768526:ONLINE Show nearby items on shelf
Title:Generalized Measure Theory [electronic resource]
Author(s): Zhenyuan Wang
George J Klir
Date:2009
Publisher:Boston, MA : Springer US
Size:1 online resource
Note:Springer e-book platform
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Note:This comprehensive text examines the relatively new mathematical area of generalized measure theory. This area expands classical measure theory by abandoning the requirement of additivity and replacing it with various weakerrequirements. Each of thes e weaker requirements characterizes a class of nonadditive measures. This results in new concepts and methods that allow us to deal with many problems in a more realistic way. For example, it allows us to workwith imprecise probabilities. The exposition o f generalized measure theory unfolds systematically. It begins with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types ofnonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerousexamples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, anextensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate lev el in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A soundbackground in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to resear chers working in the emerging area of generalized measure theory. About the Authors: ZhenyuanWang is currently a Professor in the Department of Mathematics of University of Nebraska at Omaha. His research interests have been in the areas of nonadditive me asures, nonlinear integrals, probability and statistics, and data mining.He has published one book and many papers in these areas. George J. Klir is currently a Distinguished Professor of Systems Scienc
Note:Springer eBooks
Contents:Preface
Introduction
Preliminaries
Basic Ideas of Generalized Measure Theory
Special Area of Generalized Measure Theory
Extensions
Structural Characteristics
Measurable Functions on Monotone Measure Space
Integration
Sugeno Integrals
Pan
Intergrals
Choquet Integral
Upper and Lower Integrations
Constructing Generalized Measures
Fuzzification in Generalized Measure Theory
Applications of Generalized Measure Theory
Bibliography
Appendix A. Glossary of Key Concepts
Appendix B. Glossary of Symbols
Name Index
Subject Index
ISBN:9780387768526
Series:e-books
Series:SpringerLink (Online service)
Series:IFSR International Series on Systems Science and Engineering, 1574-0463 : v25
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Systems theory , Logic, Symbolic and mathematical
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Call number:SPRINGER-2008-9788847007529:ONLINE Show nearby items on shelf
Title:Partial Differential Equations in Action [electronic resource] : From Modelling to Theory
Author(s): Sandro Salsa
Date:2008
Publisher:Milano : Springer Milan
Size:1 online resource
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Note:This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. The main purpose is on the one hand to train the students toappreciate the interp lay between theory and modelling in problems arising in the applied sciences on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbookis divided into two parts. The first one h as a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. Ideas andconnections with concrete aspects are emphasized whenever possible, in or der to provide intuition and feeling for the subject. For this part, a knowledge of advanced calculus and ordinary differential equations is required. Also, therepeated use of the method of separation of variables assumes some basic results from the theor y of Fourier series, which are summarized in an appendix. The main topic of the second part is the development of Hilbert space methods forthe variational formulation and analysis of linear boundary and initial-boundary value problems\emph{. }% Given the abstract nature of these chapters, an effort has been made to provide intuition and motivation for the various conceptsand results. The understanding of these topics requires some basic knowledge of Lebesgue measure and integration, summarized in another appendix. At the end of each chapter, a number of exercises at different level of complexity isincluded. The most demanding problems are supplied with answers or hints. The exposition if flexible enough to allow substantial changes without compromising th e comprehension and to facilitate a selection of topics for a one or twosemester course
Note:Springer eBooks
Contents:Diffusion
The Laplace Equation
Scalar Conservation Laws and First Order Equations
Waves and Vibrations
Elements of Functional Analysis
Distributions and Sobolev Spaces
Variational Formulation of Elliptic Problems
Weak Formulation of Evolution Problems
ISBN:9788847007529
Series:e-books
Series:SpringerLink (Online service)
Series:Universitext, 0172-5939
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Differential equations, partial
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Call number:SPRINGER-2008-9783764387242:ONLINE Show nearby items on shelf
Title:A Natural Introduction to Probability Theory [electronic resource]
Author(s): Ronald Meester
Date:2008
Edition:Second Edition
Publisher:Basel : Birkhuser Basel
Size:1 online resource
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Note:The book [is] an excellent new introductory text on probability. The classical way of teaching probability is based on measure theory. In this book discrete and continuous probability are studied with mathematical precision,within the realm of Rieman n integration and not using notions from measure theory. Numerous topics are discussed, such as: random walks, weak laws of large numbers, infinitely many repetitions, strong laws of large numbers,branching processes, weak convergence and [the] central li mit theorem. The theory is illustrated with many original and surprising examples and problems. Zentralblatt Math Most textbooks designed for a one-year course inmathematical statistics cover probability in the first few chapters as preparation for the st atistics to come. This book in some ways resembles the first part of such textbooks: it's all probability, no statistics. But it does theprobability more fully than usual, spending lots of time on motivation, explanation, and rigorous development of the m athematics. The exposition is usually clear and eloquent. Overall, this is a five-star book on probability thatcould be used as a textbook or as a supplement. MAA online
Note:Springer eBooks
Contents:Preface
Experiments
Random Variables and Random Vectors
Random Walk
Limit Theorems
Intermezzo
Continuous Random Variables and Vectors
Infinitely Many Repetitions
The Poisson Process
Limit Theorems
Extending the Probabilities
Interpreting Probabilities
Further Reading
Answers to Selected Exercises
Index
ISBN:9783764387242
Series:e-books
Series:SpringerLink (Online service)
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics , Distribution (Probability theory)
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Call number:SPRINGER-2008-9783764386023:ONLINE Show nearby items on shelf
Title:The Bartle-Dunford-Schwartz Integral [electronic resource] Integration with Respect to a Sigma-Additive Vector Measure
Author(s): T. V Panchapagesan
Date:2008
Publisher:Basel : Birkhuser Basel
Size:1 online resource
Note:Springer e-book platform
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Note:This volume is a thorough and comprehensive treatise on vector measures. The functions to be integrated can be either [0,infinity]- or real- or complex-valued and the vector measure can take its values in arbitrary locally convexHausdorff spaces. Mor eover, the domain of the vector measure does not have to be a sigma-algebra: it can also be a delta-ring. The book contains not only a large amount of new material but also corrects various errors in well-knownresults available in the literature. It will appeal to a wide audience of mathematical analysts
Note:Springer eBooks
Contents:Preface
1. Preliminaries
2. Basic Properties of the Bartle
Dunford
Schwartz Integral
3. Lp
Spaces
4. Integration with Respect to LcHs
valued Measures
5. Applications to Integration in Locally Compact Hausdorff Spaces I
6. Applications to Integration in Locally Compact Hausdorff Spaces II
7. Complements to the Thomas Theory of Vectorial Radon Integration
References
List of symbols
Index
ISBN:9783764386023
Series:e-books
Series:SpringerLink (Online service)
Series:Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) : v69
Series:Mathematics and Statistics (Springer-11649)
Keywords: Mathematics
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