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
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