Researched
Measure-Theoretic Probability
Lebesgue's measure and integral (1902) and Kolmogorov's axioms (1933) put probability on a rigorous footing, the base of modern statistics.
Open in the interactive tree →Henri Lebesgue's 1902 thesis extended length and the integral to a large class of sets and functions. In 1933 Andrey Kolmogorov defined a probability space as a set with a measure of total size 1 and three axioms (non-negativity, unit total, countable additivity).
Prerequisites
Unlocks
- Information Theory1948Entropy is defined on probability distributions, later put on measure-theoretic footing
- Monte Carlo Methods1949Monte Carlo estimates rest on laws of large numbers, stated rigorously in Kolmogorov's framework