Kolmogorov axioms of probability
Axiomatización de la probabilidad
- Date
- 1933 · confidence high
- Place
- Moscow, USSR
- Credited to
- Andrey Kolmogorov (Grundbegriffe der Wahrscheinlichkeitsrechnung)
- People
- 👤 Andréi Kolmogórov1903–1987
- Field
- Knowledge & symbols
What was discovered
The definition of probability as a measure of total mass 1 on a sigma-algebra, with conditional expectation and stochastic processes as consequences. It resolved Hilbert's sixth problem for probability.
Kolmogorov also founded algorithmic complexity (1965) and KAM theory.
What it led to
- stochastic processes
- Itô calculus
- ergodic theory
- mathematical statistics
- machine learning
Built on
- Measure theory and Lebesgue integral1902
- Markov chains1906
- Lebesgue measure theory
- Borel
Made possible
- Wiener–Khinchin theorem1930-1934
- Avrami equation1937-1941
- Monte Carlo method1946
- quantitative finance
- climate models