Selected Works II

1. Front Matter

   Pages i-xv

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2. On Convergence of Series Whose Terms are Determined by Random Events

   • A. Ya. Khinchin

   Pages 1-10

3. On The Law of Large Numbers

   • A. N. Shiryayev

   Pages 11-12

4. On A Limit Formula of A. Khinchin

   • A. N. Shiryayev

   Pages 13-14

5. On Sums of Independent Random Variables

   • A. N. Shiryayev

   Pages 15-31

6. On The Law of The Iterated Logarithm

   • A. N. Shiryayev

   Pages 32-42

7. On The Law of Large Numbers

   • A. N. Shiryayev

   Pages 43-47

8. 7. General Measure Theory and Probability Calculus

   • A. N. Shiryayev

   Pages 48-59

9. On The Strong Law of Large Numbers

   • A. N. Shiryayev

   Pages 60-61

10. On Analytical Methods In Probability Theory

    • A. N. Shiryayev

    Pages 62-108

11. The Waiting Problem

    • A. N. Shiryayev

    Pages 109-114

12. The Method of The Median in The Theory of Errors

    • A. N. Shiryayev

    Pages 115-117

13. A Generalization of The Laplace-Lyapunov Theorem

    • A. N. Shiryayev

    Pages 118-120

14. On The General Form of A Homogeneous Stochastic Process

    • A. N. Shiryayev

    Pages 121-127

15. On Computing The Mean Brownian Area

    • M. A. Leontovich

    Pages 128-138

16. 15. On The Empirical Determination of A Distribution Law

    • A. N. Shiryayev

    Pages 139-146

17. On The Limit Theorems of Probability Theory

    • A. N. Shiryayev

    Pages 147-155

18. On The Theory of Continuous Random Processes

    • A. N. Shiryayev

    Pages 156-168

19. On The Problem of The Suitability of Forecasting Formulas Found by Statistical Methods

    • A. N. Shiryayev

    Pages 169-175

20. Random Motions

    • A. N. Shiryayev

    Pages 176-178

The creative work of Andrei N. Kolmogorov is exceptionally wide-ranging. In his studies on trigonometric and orthogonal series, the theory of measure and inte­gral, mathematical logic, approximation theory, geometry, topology, functional analysis, classical mechanics, ergodic theory, superposition of functions, and in­ formation theory, he solved many conceptual and fundamental problems and posed new questions which gave rise to a great deal of further research. Kolmogorov is one of the founders of the Soviet school of probability theory, mathematical statistics, and the theory of turbulence. In these areas he obtained a number of central results, with many applications to mechanics, geophysics, linguistics and biology, among other subjects. This edition includes Kolmogorov's most important papers on mathematics and the natural sciences. It does not include his philosophical and ped­agogical studies, his articles written for the "Bolshaya Sovetskaya Entsiklopediya", his papers on prosody and applications of mathematics or his publications on general questions. The material of this edition was selected and compiled by Kolmogorov himself.

The first volume consists of papers on mathematics and also on turbulence and classical mechanics. The second volume is devoted to probability theory and mathematical statistics. The focus of the third volume is on information theory and the theory of algorithms.

• Estimator
• Finite
• Identity
• Median
• Normal distribution
• Probability theory
• Random variable
• Topology
• Variable
• calculus
• geometry
• mathematical statistics
• mathematics
• measure theory
• theorem

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