Verfügbarkeit: Real analysis and probability

Real analysis and probability:

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Bibliographische Detailangaben
1. Verfasser:	Dudley, Richard M. 1938- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge Cambridge Univ. Press 2002
Ausgabe:	[New Cambridge ed.]
Schriftenreihe:	Cambridge studies in advanced mathematics 74
Schlagworte:	Analyse mathématique Estruturas algébricas e topologicas Fonctions de variables réelles Probabilidade Probabilités Mathematical analysis Functions of real variables Probabilities Wahrscheinlichkeitsrechnung Analysis Reelle Funktion
Online-Zugang:	Sample text Table of contents Publisher description Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	X, 555 S.
ISBN:	052180972X 0521007542

Internformat

MARC


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Datensatz im Suchindex

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adam_text	Contents Preface to the Cambridge Edition page ix 1 Foundations; Set Theory 1 1.1 Definitions for Set Theory and the Real Number System 1 1.2 Relations and Orderings 9 * 1.3 Transfinite Induction and Recursion 12 1.4 Cardinality 16 1.5 The Axiom of Choice and Its Equivalents 18 2 General Topology 24 2.1 Topologies, Metrics, and Continuity 24 2.2 Compactness and Product Topologies 34 2.3 Complete and Compact Metric Spaces 44 2.4 Some Metrics for Function Spaces 48 2.5 Completion and Completeness of Metric Spaces 58 2.6 Extension of Continuous Functions 63 2.7 Uniformities and Uniform Spaces 67 2.8 Compactification 71 3 Measures 85 3.1 Introduction to Measures 85 3.2 Semirings and Rings 94 3.3 Completion of Measures 101 3.4 Lebesgue Measure and Nonmeasurable Sets 105 3.5 Atomic and Nonatomic Measures 109 4 Integration 114 4.1 Simple Functions 114 4.2 Measurability 123 4.3 Convergence Theorems for Integrals 130 vi Contents 4.4 Product Measures 134 4.5 Daniell-Stone Integrals 142 5 Lp Spaces; Introduction to Functional Analysis 152 5.1 Inequalities for Integrals 152 5.2 Norms and Completeness of LP 158 5.3 Hubert Spaces 160 5.4 Orthonormal Sets and Bases 165 5.5 Linear Forms on Hubert Spaces, Inclusions of LP Spaces, and Relations Between Two Measures 173 5.6 Signed Measures 178 6 Convex Sets and Duality of Normed Spaces 188 6.1 Lipschitz, Continuous, and Bounded Functionals 188 6.2 Convex Sets and Their Separation 195 6.3 Convex Functions 203 6.4 Duality of Lp Spaces 208 6.5 Uniform Boundedness and Closed Graphs 211 6.6 The Brunn-Minkowski Inequality 215 7 Measure, Topology, and Differentiation 222 7.1 Baire and Borei σ -Algebras and Regularity of Measures 222 7.2 Lebesgue s Differentiation Theorems 228 7.3 The Regularity Extension 235 7.4 The Dual of C(K) and Fourier Series 239 7.5 Almost Uniform Convergence and Lusin s Theorem 243 8 Introduction to Probability Theory 250 8.1 Basic Definitions 251 8.2 Infinite Products of Probability Spaces 255 8.3 Laws of Large Numbers 260 8.4 Ergodic Theorems 267 9 Convergence of Laws and Central Limit Theorems 282 9.1 Distribution Functions and Densities 282 9.2 Convergence of Random Variables 287 9.3 Convergence of Laws 291 9.4 Characteristic Functions 298 9.5 Uniqueness of Characteristic Functions and a Central Limit Theorem 303 9.6 Triangular Arrays and Lindeberg s Theorem 315 9.7 Sums of Independent Real Random Variables 320 Contents vii 9.8 The Levy Continuity Theorem; Infinitely Divisible and Stable Laws 325 10 Conditional Expectations and Martingales 336 10.1 Conditional Expectations 336 10.2 Regular Conditional Probabilities and Jensen s Inequality 341 10.3 Martingales 353 10.4 Optional Stopping and Uniform Integrability 358 10.5 Convergence of Martingales and Submartingales 364 10.6 Reversed Martingales and Submartingales 370 10.7 Subadditive and Superadditive Ergodic Theorems 374 11 Convergence of Laws on Separable Metric Spaces 385 11.1 Laws and Their Convergence 385 11.2 Lipschitz Functions 390 11.3 Metrics for Convergence of Laws 393 11.4 Convergence of Empirical Measures 399 11.5 Tightness and Uniform Tightness 402 1 1.6 Strassen s Theorem: Nearby Variables with Nearby Laws 406 11.7 A Uniformity for Laws and Almost Surely Converging Realizations of Converging Laws 413 11.8 Kantorovich-Rubinstein Theorems 420 11.9 ¿/-Statistics 426 12 Stochastic Processes 439 12.1 Existence of Processes and Brownian Motion 439 12.2 The Strong Markov Property of Brownian Motion 450 12.3 Reflection Principles, The Brownian Bridge, and Laws of Suprema 459 12.4 Laws of Brownian Motion at Markov Times: Skorohod Imbedding 469 12.5 Laws of the Iterated Logarithm 476 13 Measurability: Borei Isomorphism and Analytic Sets 487 13.1 Borei Isomorphism 487 13.2 Analytic Sets 493 Appendix A Axiomatic Set Theory 503 A. 1 Mathematical Logic 503 A.2 Axioms for Set Theory 505 viii Contents А.З Ordinals and Cardinals 510 A.4 From Sets to Numbers 515 Appendix В Complex Numbers, Vector Spaces, and Taylor s Theorem with Remainder 521 Appendix С The Problem of Measure 526 Appendix D Rearranging Sums of Nonnegative Terms 528 Appendix E Pathologies of Compact Nonmetric Spaces 530 Author Index 541 Subject Index 546 Notation Index 554
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spellingShingle	Dudley, Richard M. 1938- Real analysis and probability Cambridge studies in advanced mathematics Analyse mathématique Estruturas algébricas e topologicas larpcal Fonctions de variables réelles Probabilidade larpcal Probabilités Mathematical analysis Functions of real variables Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Analysis (DE-588)4001865-9 gnd Reelle Funktion (DE-588)4048918-8 gnd
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title	Real analysis and probability
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title_full	Real analysis and probability R. M. Dudley
title_fullStr	Real analysis and probability R. M. Dudley
title_full_unstemmed	Real analysis and probability R. M. Dudley
title_short	Real analysis and probability
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topic	Analyse mathématique Estruturas algébricas e topologicas larpcal Fonctions de variables réelles Probabilidade larpcal Probabilités Mathematical analysis Functions of real variables Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Analysis (DE-588)4001865-9 gnd Reelle Funktion (DE-588)4048918-8 gnd
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