This fourth edition contains several additions．The main ones concern three closely related topics：Brownian motion．functional Jimit distributions，and random walks．Besides the power and ingenuity of their methods and the depth and beauty of their results，their importance is fast growing in Analysis as well as in theoretical and applied Probability．

这是一套公认的概率论经典教科书，可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专家、学者经常使用的参考书。在这套书的第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，后两部尤为精彩。

INTRODUCTORY PART: ELEMENTARY PROBABILITY THEORY

SECTION

Ⅰ.INTUITIVE BACKGROUND

 1.Events

 2.Random events and trials

 3.Random variables

Ⅱ.AXIOMS； INDEPENDENCE AND THE BERNOULLI CASE

 1.Axioms of the finite case

 2.Simple random variables

 3.Independence

 4.Bernoulli case

 5.Axioms for the countable case

 6.Elementary random variables

 7.Need for nonelementary random variables

Ⅲ.DEPENDENCE AND CHAINS

 1.Conditional probabilities

 2.Asymptotically Bernoullian case

 3.Recurrence

 4.Chain dependence

 5.Types of states and asymptotic behavior

 6.Motion of the system

 7.Stationary chains

COMLEMENTS AND DETAILS

PART ONE:NOTIONS OF MEASURE THEORY

CHAPTERⅠ:SETS,SPACES,AND MEASURES

 1.SETS,CLASSES,AND FUNCTIONS

 2.TOPOLOGICAL SPACES

 3.ADDITIVE SET FUNCTIONS

 4.CONSTRUCTION OF MEASURES ONFIELDS

CHAPTERⅡ:MEASURABLE FUNCTIONS AND INTEGRATION

 5.MEASURABLE FUNCTIONS

 6.MEASURE AND CONVERGENCES

 7.INTEGRATION

 8.INDEFINITE INTEGRALS;ITERATED INTEGRALS

PART TWO:GENERAL CONCEPTS AND TOOLS OF PROBABILITY THEORY

CHAPTERⅢ:PROBABILITY CONCEPTS

 9.PROBABILITY SPACES AND RANDOM VARIABLES

 10.PROBABILITY DISTRIBUTIONS

CHAPTERⅣ:DISTRIBUTION FUNCTIONS AND CHARACTERISTIC FUNCTIONNS

 11.DISTRIBUTION FUNCTIONS

 12.CONVERGENCE OF PROBABILITIES ON METRIC SPACES

 13.CHARACTERISTIC FUNCTIONS AND DISTRIBUTION FUNCTIONS

 14.PROBABILITY LAWS AND TYPES OF LAWS

 15.NONNEGATIVE-DEFINITENESS;REGULARITY

PART THREE:INDEPENDENCE

CHAPTERⅤ:SUMS OF INDEPENDENT RANDOM VARIABLES

 16.CONCEPT OF INDEPENDENCE

 17.CONVERGENCE AND STABILITY OF SUMS;CENTERING AT

 18.CONVERGENCE AND SABILTIY OF SUMS;CENTERING AT

 19.EXPONENTIAL BOUNDS AND NORMED SUMS

CHAPTERⅥ:ENTRAL LIMIT PROBLEM

 20.DEGENERATE,NORMAL AND POISSON TYPES

 21.EVOLUTION OF THE PROBLEM

 22.CENTRAL LIMIT PROBLEM;THE CASE OF BOUNDED VARIANCES

 23.SOLUTION OF THE ENTRAL LIMIT PROBLEM

 24.NORMED SUMS

CHAPTERⅦ:INDEPENDENT IDENTICALLY DISTRIBUTED SUMMANDS

 25.REGULAR VARIATION AND DOMAINS OF ATTRACTION

 26.RANDOM WALK

BIBLIOGRAPHY

INDEX

DEPENDENCE

ELEMENTS OF RANDOM ANALYSIS