Random Variables and Probability Distributions

This tract develops the purely mathematical side of the theory of probability.

Preface to the first edition; Preface to the second edition; Preface to the third edition; Abbreviations; Part I. Principles: 1. Introductory remarks; 2. Axioms and preliminary theorems; Part II. Distributions in R1: 3. General properties; 4. Characteristic functions; 5. Addition of independent variables; 6. The normal distribution and the central limit theorem; 7. Error estimation; 8. A class of stochastic processes; Part III. Distributions in R2: 9. General properties; 10. The normal distribution and the central limit theorem; Bibliography.