"A Course in Probability Theory" by Kai Lai Chung
Third Edition
Academic Press | 2001 | ISBN: 0121741516 9780121741518 9780080522982 | 433 pages | PDF/djvu | 18/10 MB

This book is considered a classic, original work in probability theory due to its elite level of sophistication. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current Course in Probability Theory.

Contents
Preface to the third edition
Preface to the second edition
Preface to the first edition
1 Distribution function
1.1 Monotone functions
1.2 Distribution functions
1.3 Absolutely continuous and singular distributions
2 Measure theory
2.1 Classes of sets
2.2 Probability measures and their distribution functions
3 Random variable. Expectation. Independence
3.1 General definitions
3.2 Properties of mathematical expectation
3.3 Independence
4 Convergence concepts
4.1 Various modes of convergence
4.2 Almost sure convergence ; Borel-Cantelli lemma
4.3 Vague convergence
4.4 Continuation
4.5 Uniform integrability ; convergence of moments
5 Law of large numbers. Random series
5.1 Simple limit theorems
5.2 Weak law of large numbers
5.3 Convergence of series
5.4 Strong law of large numbers
5.5 Applications
Bibliographical Note
6 Characteristic function
6.1 General properties ; convolutions
6.2 Uniqueness and inversion
6.3 Convergence theorems
6.4 Simple applications
6.5 Representation theorems
6.6 Multidimensional case ; Laplace transforms
Bibliographical Note
7 Central limit theorem and its ramifications
7.1 Liapounov's theorem
7.2 Lindeberg-Feller theorem
7.3 Ramifications of the central limit theorem
7.4 Error estimation
7.5 Law of the iterated logarithm
7.6 Infinite divisibility
Bibliographical Note
8 Random walk
8.1 Zero-or-one laws
8.2 Basic notions
8.3 Recurrence
8.4 Fine structure
8.5 Continuation
Bibliographical Note
9 Conditioning. Markov property. Martingale
9.1 Basic properties of conditional expectation
9.2 Conditional independence ; Markov property
9.3 Basic properties of smartingales
9.4 Inequalities and convergence
9.5 Applications
Bibliographical Note
Supplement: Measure and Integral
1 Construction of measure
2 Characterization of extensions
3 Measures in R
4 Integral
5 Applications
General Bibliography
Index