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实分析和概率论 第2版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）达德利（Dudley，R.M.）著 著
- 出版社： 北京：机械工业出版社
- ISBN：7111193482
- 出版时间：2006
- 标注页数：555页
- 文件大小：104MB
- 文件页数：565页
- 主题词：实分析－英文；概率论－英文
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图书目录
1 Foundations;Set Theory1
1.1 Definitions for Set Theory and the Real Number System1
1.2 Relations and Orderings9
1.3 Transfinite Induction and Recursion12
1.4 Cardinality16
1.5 The Axiom of Choice and Its Equivalents18
2 General Topology24
2.1 Topologies,Metrics,and Continuity24
2.2 Compactness and Product Topologies34
2.3 Complete and Compact Metric Spaces44
2.4 Some Metrics for Function Spaces48
2.5 Completion and Completeness of Metric Spaces58
2.6 Extension of Continuous Functions63
2.7 Uniformities and Uniform Spaces67
2.8 Compactification71
3 Measures85
3.1 Introduction to Measures85
3.2 Semirings and Rings94
3.3 Completion of Measures101
3.4 Lebesgue Measure and Nonmeasurable Sets105
3.5 Atomic and Nonatomic Measures109
4 Integration114
4.1 Simple Functions114
4.2 Measurability123
4.3 Convergence Theorems for Integrals130
4.4 Product Measures134
4.5 Daniell-Stone Integrals142
5 Lp Spaces;Introduction to Functional Analysis152
5.1 Inequalities for Integrals152
5.2 Norms and Completeness of Lp158
5.3 Hilbert Spaces160
5.4Orthonormal Sets and Bases165
5.5 LinearForms on Hilbert Spaces,Inclusions of Lp Spaces,and Relations Between Two Measures173
5.6 Signed Measures178
6 Convex Sets and Duality of Normed Spaces188
6.1 Lipschitz,Continuous,and Bounded Functionals188
6.2 Convex Sets and Their Separation195
6.3 Convex Functions203
6.4 Duality of Lp Spaces208
6.5 Uniform Boundedness and Closed Graphs211
6.6 The Brunn-Minkowski Inequality215
7 Measure,Topology,and Differentiation222
7.1 Baire and Borel σ-Algebras and Regularity of Measures222
7.2 Lebesgue's Differentiation Theorems228
7.3 The Regularity Extension235
7.4 The Dual of C(K)and Fourier Series239
7.5 Almost Uniform Convergence and Lusin's Theorem243
8 Introduction to Probability Theory250
8.1 Basic Definitions251
8.2 Infinite Products of Probability Spaces255
8.3 Laws of Large Numbers260
8.4 Ergodic Theorems267
9 Convergence of Laws and Central Limit Theorems282
9.1 Distribution Functions and Densities282
9.2 Convergence of Random Variables287
9.3 Convergence of Laws291
9.4 Characteristic Functions298
9.5 Uniqueness of Characteristic Functions and a Central Limit Theorem303
9.6 Triangular Arrays and Lindeberg's Theorem315
9.7 Sums of Independent Real Random Variables320
9.8 The Lévy Continuity Theorem;Infinitely Divisible and Stable Laws325
10 Conditional Expectations and Martingales336
10.1 Conditional Expectations336
10.2 Regular Conditional Probabilities and Jensen's Inequality341
10.3 Martingales353
10.4 Optional Stopping and Uniform Integrability358
10.5 Convergence of Martingales and Submartingales364
10.6 Reversed Martingales and Submartingales370
10.7 Subadditive and Superadditive Ergodic Theorems374
11 Convergence of Laws on Separable Metric Spaces385
11.1 Laws and Their Convergence385
11.2 Lipschitz Functions390
11.3 Metrics for Convergence of Laws393
11.4 Convergence of Empirical Measures399
11.5 Tightness and Uniform Tightness402
11.6 Strassen's Theorem:Nearby Variables with Nearby Laws406
11.7 A Uniformity for Laws and Almost Surely Converging Realizations of Converging Laws413
11.8 Kantorovich-Rubinstein Theorems420
11.9 U-Statistics426
12 Stochastic Processes439
12.1 Existence of Processes and Brownian Motion439
12.2 The Strong Markov Property of Brownian Motion450
12.3 Reflection Principles,The Brownian Bridge,and Laws of Suprema459
12.4 Laws of Brownian Motion at Markov Times:Skorohod Imbedding469
12.5 Laws of the Iterated Logarithm476
13 Measurability:Borel Isomorphism and Analytic Sets487
13.1 Borel Isomorphism487
13.2 Analytic Sets493
Appendix A Axiomatic Set Theory503
A.1 Mathematical Logic503
A.2 Axioms for Set Theory505
A.3 Ordinals and Cardinals510
A.4 From Sets to Numbers515
Appendix B Complex Numbers,Vector Spaces,and Taylor's Theorem with Remainder521
Appendix C The Problem of Measure526
Appendix D Rearranging Sums of Nonnegative Terms528
Appendix E Pathologies of Compact Nonmetric Spaces530
Author Index541
Subject Index546
Notation Index554