VOLUME 1
Ⅰ. INTUITIVE BACKGROUND
1. Events
2. Random events and trials
3. Random variables
Ⅱ. AXIOMS; INDEPENDENCE AND THE BERN ULLI CASE
1. Axioms of the finite case
2. Simple random variables
3. Independence
4. Bernoulli case
5. Axioms for the countable cast
6. Elementary random variable,s
7. Need for nonelementary random wariables
Ⅲ. DEPENDENCE AND CHAINS
1. Conditional probabilities
2. Asymptotically Bernoullian ctse
3. Recurrence
4. Chain dependence
* 5. Types of states and asympto'ti~ l:eh atvior
* 6. Motion of the system
* 7. Stationary chains .
COMPLEMENTS AND DETAILS
PART ONE: NOTIONS OF MEASURE THEORY
CHAPTER I: SETS, SPACES, AND MEASURES
1. SETS, CLASSES, AND FUNCTIONS
1.1 Definitions and notations
1.2 Differences, unions, and intersections
1.3 Sequences and limits
1.4 Indicators of sets
1.5 Fields and a-fields
1.6 Monotone classes
*1.7 Product sets
*1.8 Functions and inverse functions
*1.9 Measurable spaces and functions
*2. TOPOLOGICAL SPACES .
*2.1 Topologies and limits
*2.2 Limit points and compact spaces
*2.3 Countability and metric spaces
*2.4 Linearity and normed spaces
3. ADDITIVE SET FUNCTIONS
3.1 Additivity and continuity
3.2 Decomposition of additive set functions
*4. CONSTRUCTION Of MEASURES ON #-FIELDS
*4.1 Extension of measures
*4.2 Product probabilities
*4.3 Consistent probabilities on Borel fields
*4.4 Lebesgue-Stieltjes measures and distribution functions
COMPLEMENTS AND DETAILS
CHAPTER II: MEASURABLE FUNCTIONS AND INTEGRATION
5. MEASURABLE FUNCTIONS
5.1 Numbers
5.2 Numerical functions
5.3 Measurable functions
6. MEASURE AND CONVERGENCES
6.1 Definitions and general properties
6.2 Convergence almost everywhere
6.3 Convergence in measure
7. INTEGRATION
7.1 Integrals
7.2 Convergence theorems
8. INDEFINITE INTEGRALS; ITERATED INTEGRALS
8.1 Indefinite integrals and Lcbcsgue decomposition
8.2 Product measures and iterated integrals
*8.3 Iterated integrals and infinite product spaces
……
PART TWO: GENERAL CONCEPTS AND TOOLS OF PROBALITY THEORY
PART THREE: INDEPENDENCE
BIBLIOGRAPHY
INDEX
VOLUME Ⅱ
DEPENDENCE
ELEMENTS OF RANDOM ANALYSIS
BIBLIOGRAPHY
INDEX

本书被公认为是一套概率论方面的标准经典教科书，供高年级大学生和研究生使用，同时也是概率论和统计学方面研究人员经常使用的参考书。本书把概率论建立在严格的逻辑基础上，理论体系完整。在第4版中增加了距离空间测定、随机游动、布朗运动及不变原理四部分，后两部分尤为精彩。全书除引言外，两卷共分五部分，第1卷包括三部分，涉及概率论的基本概念和数学手段。读者对象：数学及相关专业的研究生。