ProofWiki:Mathematicians/Andrey Kolmogorov
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Andrey Nikolaevich Kolmogorov (Russian: Андрей Николаевич Колмогоров) was a Russian mathematician active in various fields, including probability theory, topology and intuitionistic logic.
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Nationality
Russian
History
- Born: April 25, 1903, Tambov, Russia
- Died: October 20, 1987, Moscow, Russia
Theorems and Definitions
- Kolmogorov Axioms
- Kolmogorov-Arnold-Moser Theorem (with Vladimir Igorevich Arnold and Jürgen Kurt Moser)
- Kolmogorov Backward Equation
- Kolmogorov Forward Equation (also known as the Fokker-Planck Equation)
- Kolmogorov dimension (upper box dimension)
- Kolmogorov Continuity Theorem
- Kolmogorov's Criterion
- Kolmogorov's Generalized Criterion
- Kolmogorov Extension Theorem
- Kolmogorov's Inequality
- Landau-Kolmogorov Inequality (with Edmund Landau)
- Brouwer-Heyting-Kolmogorov Interpretation (independently of Bertus Brouwer and Arend Heyting)
- Kolmogorov Microscales
- Kolmogorov Space (also known as a $T_0$ Space)
- Kolmogorov Complexity
- Kolmogorov-Smirnov Test (with Vladimir Ivanovich Smirnov)
- Kolmogorov's Zero-One Law
- Kolmogorov's Characterization of Reversible Diffusions
- Borel-Kolmogorov Paradox (with Émile Borel)
- Chapman-Kolmogorov Equation (with Sydney Chapman)
- Chaitin-Kolmogorov Randomness (with Gregory John Chaitin)
- Hahn-Kolmogorov Theorem (with Hans Hahn)
Books and Papers
- 1925: On the principle of the excluded middle
- 1931: About the Analytical Methods of Probability Theory
- 1933: Grundbegriffe der Wahrscheinlichkeitsrechnung (Foundations of the Theory of Probability)
- 1938: Analytic methods in probability theory
- 1968: Introductory Real Analysis (with Sergei Fomin) (translated into English, and rather severely and less-than-successfully edited, in 1970 by Richard A. Silverman, Dover Publications: ISBN 0-486-61226-0)
