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全新正版概率论入门(英文版)9787510058271世界图书出版公司
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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 Oraios 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
. 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 Coition
3.2.2 Random Elements of Metric Spaces
3.. MeasurabiliyndCntinuity
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 Kooorov Zero-One Law
4.6 Exercises
5 Integration and Expectation
5.1 Preparation for Integration
5.1.1 Simple Functions
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