Andrey Kolmogorov

Andrey Kolmogorov (1903–1987) was a Soviet mathematician whose work established modern probability theory and advanced turbulence, information theory, and mathematical logic.

Probability theory: The mathematical study of random events, uncertainty, and the patterns they produce. Kolmogorov gave probability theory its modern axiomatic foundation.
Kolmogorov axioms: Three axioms defining probability through a normalized, countably additive measure on events. They are the central formal result associated with his name.
Kolmogorov turbulence theory: A statistical theory describing energy transfer and scaling in fully developed turbulence at high Reynolds numbers. His 1941 theory predicts universal scaling laws for turbulent velocity differences.
Nikolai Luzin: A Russian mathematician who founded the Moscow school of descriptive set theory and real analysis. Luzin supervised Kolmogorov’s early mathematical development at Moscow State University.
Foundations of probability: The study of the basic assumptions and interpretations on which probability theory rests. Kolmogorov’s axioms became the dominant mathematical foundation for probability.
Measure theory: The mathematical framework for assigning sizes to sets, including lengths, areas, and probabilities. Its language let Kolmogorov define probability rigorously on general event spaces.
Kolmogorov extension theorem: A theorem establishing a stochastic process from consistent probability distributions on finite collections of coordinates. It explains how finite-dimensional distributions can specify an entire random process.
Kolmogorov–Arnold–Moser theorem: A theorem showing that many invariant tori in integrable Hamiltonian systems survive sufficiently small perturbations. Kolmogorov initiated the result on the persistence of quasi-periodic motion.
Alexander Khinchin: A Soviet mathematician known for work in probability, number theory, and statistical physics. Khinchin was a close collaborator in the development of modern probability.
Algorithmic randomness: A family of definitions of randomness based on effective tests or incompressibility. Kolmogorov’s complexity inspired a rigorous account of randomness for individual sequences.

Linked from 22 pages