概率与测度论（英文版 第2版）
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 Ri…
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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 Ri…
查看完整
Robert B.Ash，伊利诺大学数学系教授。世界著名数学家，研究领域包括：信息理论、代数、拓扑、概率论、泛函分析等。主要著作有Measure，Integration and Functional Analysis和Information Theory等。
《概率与测度论（英文版）（第2版）》是测度论和概率论领域的名著，行文流畅，主线清晰，材料取舍适当，内容包括测度和积分论、泛函分析、条件概率和期望、强大数定理和鞅论、中心极限定理、遍历定理以及布朗运动和随机积分等，全书各节都附有习题，而且在书后提供了大部分习题的详细解答。
《概率与测度论（英文版）（第2版）》可作为相关专业高年级本科生或研究生的双语教材，适合作为一学年的教学内容，也可选用其中部分章节用作一学期的教学内容或参考书。
《概率与测度论（英文版）（第2版）》可作为相关专业高年级本科生或研究生的双语教材，适合作为一学年的教学内容，也可选用其中部分章节用作一学期的教学内容或参考书。
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
^ 收 起
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
^ 收 起
Robert B.Ash，伊利诺大学数学系教授。世界著名数学家，研究领域包括：信息理论、代数、拓扑、概率论、泛函分析等。主要著作有Measure，Integration and Functional Analysis和Information Theory等。
《概率与测度论（英文版）（第2版）》是测度论和概率论领域的名著，行文流畅，主线清晰，材料取舍适当，内容包括测度和积分论、泛函分析、条件概率和期望、强大数定理和鞅论、中心极限定理、遍历定理以及布朗运动和随机积分等，全书各节都附有习题，而且在书后提供了大部分习题的详细解答。
《概率与测度论（英文版）（第2版）》可作为相关专业高年级本科生或研究生的双语教材，适合作为一学年的教学内容，也可选用其中部分章节用作一学期的教学内容或参考书。
《概率与测度论（英文版）（第2版）》可作为相关专业高年级本科生或研究生的双语教材，适合作为一学年的教学内容，也可选用其中部分章节用作一学期的教学内容或参考书。
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