文档介绍：A
COURSE IN
PROBABILITY
THEORY
THIRD EDITION
A
COURSE IN
PROBABILITY
THEORY
THIRD EDITION
Kai Lai Chung
Stanford University
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Contents
Preface to the third edition ix
Preface to the second edition xi
Preface to the first edition xiii
1 J Distribution function
1 .1 Monotone functions 1
1 .2 Distribution functions 7
1 .3 Absolutely continuous and singular distributions 11
2 I Measure theory
2 .1 Classes of sets 16
Probability measures and their distribution
functions 21
3 1 Random variable . Expectation . Independence
General definitions 34
Properties of mathematical expectation 41
Independence 53
4 Convergence concepts
Various modes of convergence 68
Almost sure convergence ; Borel-Cantelli lemma 75
vi I CONTENTS
4 .3 Vague convergence 84
4 .4 Continuation 91
4 .5 Uniform integrability ; convergence of mom