Selected Works III Information Theory and the Theory of Algorithms

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.

Papers by A. V. Kolmogorov.- 1. On the notion of algorithm.- 2. On the general definition of the quantity of information.- 3. The theory of transmission of information.- 4. Amount of information and entropy for continuous distributions.- 5. New metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces.- 6. To the definition of algorithms.- 7. ?-entropy and ?-capacity of sets in functional spaces.- 8. Various approaches to estimating the complexity of approximate representation and calculation of functions.- 9. On tables of random numbers.- 10. Three approaches to the definition of the notion of amount of information.- 11. On the realization of networks in three — dimensional space.- 12. To the logical foundations of the theory of information and probability theory.- 13. The combinatorial foundations of information theory and the probability calculus.- Comments and addenda.- On works in information theory and some of its applications.- Information theory.- Algorithmic information theory.- ?-entropy and ?-capacity.- Tables of random numbers.- Realization of networks in 3-dimensional space.- Ergodic theory.- Kolmogorov’s algorithms or machines.- From A. N. Kolmogorov’s recollections.- Appendix 1. Report to the mathematical circle about square pavings.- Appendix 2. On operations on sets. II.- Afterword.