《機率與測度論》是2007年人民郵電出版社出版的圖書，作者是RobertB.Ash。
基本介紹
- 書名：機率與測度論
- 作者：美RobertB.Ash
- ISBN：9787115166159
- 頁數：516
- 定價：69.00元
- 出版社：人民郵電出版社
- 出版時間：2007-9
- 裝幀：平裝
- 開本：16
- 叢書：圖靈原版數學·統計學系列
內容簡介,作者簡介,目錄,
內容簡介
《機率與測度論(英文版 第2版)》是測度論和機率論領域的名著，行文流暢，主線清晰，材料取捨適當，內容包括測度和積分論、泛函分析、條件機率和期望、強大數定理和鞅論、中心極限定理、遍歷定理以及布朗運動和隨機積分等，全書各節都附有習題，而且在書後提供了大部分習題的詳細解答。
《機率與測度論(英文版 第2版)》可作為相關專業高年級本科生或研究生的雙語教材，適合作為一學年的教學內容，也可選用其中部分章節用作一學期的教學內容或參考書。
作者簡介
Robert B.Ash，伊利諾大學數學系教授。世界著名數學家，研究領域包括：信息理論、代數、拓撲、機率論、泛函分析等。主要著作有Measure，Integration and Functional Analysis和Information Theory等。
目錄
1 Fundamentals of Measure and Integration Theory
1.1 Introduction
1.2 Fields, o-Fields, and Measures
1.3 Extension of Measures
1.4 Lebesgue-Stieltjes Measures and Distribution Functi
1.5 Measurable Functions and Integration
1.6 Basic Integration Theorems
1.7 Comparison of Lebesgue and Riemann Integrals
2 Further Results in Measure and Integration Theory
2.1 Introduction
2.2 Radon-Nikodym Theorem and Related Results
2.3 Applications to Real Analysis
2.4 Lp Spaces
2.5 Convergence of Sequences of Measurable Functions
2.6 Product Measures and Fubinis Theorem
2.7 Measures on Infinite Product Spaces
2.8 Weak Convergence of Measures
2.9 References
3 Introduction to Functional Analysis
3.1 Introduction
3.2 Basic Properties of Hilbert Spaces
3.3 Linear Operators on Normed Linear Spaces
3.4 Basic Theorems of Functional Analysis
3.5 References
4 Basic Concepts of Probability
4.1 Introduction
4.2 Discrete Probability Spaces
4.3 Independence
4.4 Bernoulli Trials
4.5 Conditional Probability
4.6 Random Variables
4.7 Random Vectors
4.8 Independent Random Variables
4.9 Some Examples from Basic Probability
4.10 Expectation
4.11 Infinite Sequences of Random Variables
4.12 References
5 Conditional Probability and Expectation
5.1 Introduction
5.2 Applications
5.3 The General Concept of Conditional Probability and Expectation
5.4 Conditional Expectation Given a o-Field
5.5 Properties of Conditional Expectation
5.6 Regular Conditional Probabilities
6 Strong Laws of Large Numbers and Martingale Theory
6.1 Introduction
6.2 Convergence Theorems
6.3 Martingales
6.4 Martingale Convergence Theorems
6.5 Uniform Integrability
6.6 Uniform Integrability and Martingale Theory
6.7 Optional Sampling Theorems
6.8 Applications of Martingale Theory
6.9 Applications to Markov Chains
6.10 References
7 The Central Limit Theorem
7.1 Introduction
7.2 The Fundamental Weak Compactness Theorem
7.3 Convergence to a Normal Distribution
……
8 Ergodic Theory
9 Brownian Motion and Stochastic Integrals
Appendices
Bibliography
Solutions to Problems
Index
1.1 Introduction
1.2 Fields, o-Fields, and Measures
1.3 Extension of Measures
1.4 Lebesgue-Stieltjes Measures and Distribution Functi
1.5 Measurable Functions and Integration
1.6 Basic Integration Theorems
1.7 Comparison of Lebesgue and Riemann Integrals
2 Further Results in Measure and Integration Theory
2.1 Introduction
2.2 Radon-Nikodym Theorem and Related Results
2.3 Applications to Real Analysis
2.4 Lp Spaces
2.5 Convergence of Sequences of Measurable Functions
2.6 Product Measures and Fubinis Theorem
2.7 Measures on Infinite Product Spaces
2.8 Weak Convergence of Measures
2.9 References
3 Introduction to Functional Analysis
3.1 Introduction
3.2 Basic Properties of Hilbert Spaces
3.3 Linear Operators on Normed Linear Spaces
3.4 Basic Theorems of Functional Analysis
3.5 References
4 Basic Concepts of Probability
4.1 Introduction
4.2 Discrete Probability Spaces
4.3 Independence
4.4 Bernoulli Trials
4.5 Conditional Probability
4.6 Random Variables
4.7 Random Vectors
4.8 Independent Random Variables
4.9 Some Examples from Basic Probability
4.10 Expectation
4.11 Infinite Sequences of Random Variables
4.12 References
5 Conditional Probability and Expectation
5.1 Introduction
5.2 Applications
5.3 The General Concept of Conditional Probability and Expectation
5.4 Conditional Expectation Given a o-Field
5.5 Properties of Conditional Expectation
5.6 Regular Conditional Probabilities
6 Strong Laws of Large Numbers and Martingale Theory
6.1 Introduction
6.2 Convergence Theorems
6.3 Martingales
6.4 Martingale Convergence Theorems
6.5 Uniform Integrability
6.6 Uniform Integrability and Martingale Theory
6.7 Optional Sampling Theorems
6.8 Applications of Martingale Theory
6.9 Applications to Markov Chains
6.10 References
7 The Central Limit Theorem
7.1 Introduction
7.2 The Fundamental Weak Compactness Theorem
7.3 Convergence to a Normal Distribution
……
8 Ergodic Theory
9 Brownian Motion and Stochastic Integrals
Appendices
Bibliography
Solutions to Problems
Index
