Selected Works III

1. Front Matter

   Pages i-xxv

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2. Papers by A. N. Kolmogorov

   1. On the Notion of Algorithm

      • A. N. Shiryayev

      Pages 1-1

   2. On the General Definition of the Quantity of Information

      • I. M. Gelfand, A. M. Yaglom

      Pages 2-5

   3. The Theory of Transmission of Information

      • A. N. Shiryayev

      Pages 6-32

   4. Amount of Information and Entropy for Continuous Distributions

      • I. M. Gelfand, A. M. Yaglom

      Pages 33-56

   5. New Metric Invariant of Transitive Dynamical Systems and Automorphisms of Lebesgue Spaces

      • A. N. Shiryayev

      Pages 57-61

   6. To the Definition of Algorithms

      • V. A. Uspenski

      Pages 62-85

   7. ε-Entropy and ε-Capacity of Sets In Functional Spaces

      • V. M. Tikhomirov

      Pages 86-170

   8. Various Approaches to Estimating the Complexity of Approximate Representation and Calculation of Functions

      • A. N. Shiryayev

      Pages 171-175

   9. On Tables of Random Numbers

      • A. N. Shiryayev

      Pages 176-183

   10. Three Approaches to the Definition of the Notion of Amount of Information

       • A. N. Shiryayev

       Pages 184-193

   11. On the Realization of Networks in Three-Dimensional Space

       • Ya. M. Barzdin

       Pages 194-202

   12. To the Logical Foundations of the Theory of Information and Probability Theory

       • A. N. Shiryayev

       Pages 203-207

   13. The Combinatorial Foundations of Information Theory and the Probability Calculus

       • A. N. Shiryayev

       Pages 208-218

3. Comments and addenda

   1. On Works in Information Theory and some of Its Applications

      • A. N. Kolmogorov

      Pages 219-221

   2. Information Theory

      • R. L. Dobrushin

      Pages 222-225

   3. Algorithmic Information Theory

      • A. Kh. Shen

      Pages 226-230

   4. ε-Entropy and ε-Capacity

      • V. M. Tikhomirov

      Pages 231-239

   5. Tables of Random Numbers

      • A. Sh. Shen

      Pages 240-244

   6. Realization of Networks in 3-Dimensional Space

      • Ya. M. Barzdin

      Pages 245-246

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.

• Invariant
• Morphism
• algorithmic information theory
• calculus
• complexity
• entropy
• function
• information theory

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