概率论入门(英文版)

本书是一部十分经典的 概率论教程。1999年初版 ，2001年第2次重印，2003 年第3次重印，同年第4次重 印，2005年第5次重印，受 欢迎程度可见一斑。大多数 概率论书籍是写给数学家看 的，漂亮的数学材料是吸引 读者的一大亮点；相反地， 本书目标读者是数学及非数 学专业的研究生，帮助那些 在统计、应用概率论、生物 、运筹学、数学金融和工程 研究中需要深入了解高等概 率论的所有人员。

Preface 1 Sets and Events 1.1 Introduction 1.2 Basic Set Theory 1.2.1 Indicator functions 1.3 Limits of Sets 1.4 Monotone Sequences 1.5 Set Operations and Closure 1.5.1 Examples 1.6 The σ-field Generated by a Given Class C 1.7 Borel Sets on the Real Line 1.8 Comparing Borel Sets 1.9 Exercises 2 Probability Spaces 2.1 Basic Definitions and Properties 2.2 More on Closure 2.2.1 Dynkin's theorem 2.2.2 Proof of Dynkin's theorem 2.3 Two Constructions 2.4 Constructions of Probability Spaces 2.4.1 General Construction of a Probability Model 2.4.2 Proof of the Second Extension Theorem 2.5 Measure Constructions 2.5.1 Lebesgue Measure on (0,1] 2.5.2 Construction of a Probability Measure on R with Given Distribution Function F(x) 2.6 Exercises 3 Random Variables,Elements,and Measurable Maps 3.1 Inverse Maps 3.2 Measurable Maps,Random Elements, Induced Probability Measures 3.2.1 Composition 3.2.2 Random Elements of Metric Spaces 3.2.3 Measurability and Continuity 3.2.4 Measurability and Limits 3.3 σ-Fields Generated by Maps 3.4 Exercises 4 Independence 4.1 Basic Definitions 4.2 Independent Random Variables 4.3 Two Examples of Independence 4.3.1 Records,Ranks,Renyi Theorem 4.3.2 Dyadic Expansions of Uniform Random Numbers 4.4 More on Independence:Groupings 4.5 Independence,Zero-One Laws,Borel-Cantelli Lemma 4.5.1 Borel-Cantelli Lemma 4.5.2 Borel Zero-One Law 4.5.3 Kolmogorov Zero-One Law 4.6 Exercises 5 Integration and Expectation 5.1 Preparation for Integration 5.1.1 Simple Functions