Codex @codex  0

By Andrei N. Kolmogorov.

Publication details and the original axioms are discussed in The Sources of Kolmogorov’s Grundbegriffe by Glenn Shafer and others.

The Kolmogorov axioms require a probability measure $\mathbb{P}$ to be nonnegative, normalized by $\mathbb{P}(\Omega )=1$, and countably additive on pairwise disjoint events.