Foundations of the theory of probability

Title page
EDITOR'S NOTE
PREFACE
I. ELEMENTARY THEORY OF PROBABILITY
1. Axioms
2. The relation to experimental data
3. Notes on terminology
4. Immediate corollaries of the axioms; conditional probabilities; Theorem of Bayes
5. Independence
6. Conditional probabilities as random variables; Markov chains
II. INFINITE PROBABILITY FIELDS
1. Axiom of Continuity
2. Borel fields of probability
3. Examples of Infinite fields of probability
III. RANDOM VARIABLES
1. Probability functions
2. Definition of random variables and of distribution functions
3. Multi-dimensional distribution functions
4. Probabilities in infinite-dimensional spaces
5. Equivalent random variables; various kinds of convergence
IV. MATHEMATICAL EXPECTATIONS
1. Abstract Lebesgue integrals
2. Absolute and conditional mathematical expectations
3. The Tchebycheff inequality
4. Some criteria for convergence
5. Differentiation and integration of mathematical expectations with respect to a parameter
V. CONDITIONAL PROBABILITIES AND MATHEMATICAL EXPECTATIONS
1. Conditional probabilities
2. Explanation of a Borel paradox
3. Conditional probabilities with respect to a random variable
4. Conditional mathematical expectations
VI. INDEPENDENCE; THE LAW OF LARGE NUMBERS
1. Independence
2. Independent random variables
3. The Law of Large Numbers
4. Notes on the concept of mathematical expectation
5. The Strong Law of Large Numbers; convergence of a series
APPENDIX-Zero-or-one law in the theory of probability
BIBLIOGRAPHY
NOTES TO SUPPLEMENTARY BIBLIOGRAPHY
SUPPLEMENTARY BIBLIOGRAPHY