Kolmogorov's axioms

Whatever interpretation we give to probability, it must obey a few basic rules, formalised by the Russian mathematician Andrey Kolmogorov. From these three axioms the whole of probability theory follows.

Property — Kolmogorov's axioms

A probability function $P$ on events satisfies:

1. $0 \le P(E) \le 1$ for every event $E$;
2. $P(\Omega) = 1$ (the sample space is certain);
3. $P(E_1 \cup E_2) = P(E_1) + P(E_2)$ if $E_1$ and $E_2$ are mutually exclusive (that is, $E_1 \cap E_2 = \emptyset$).

The third axiom, called the additivity axiom, extends to any number of pairwise mutually exclusive events.

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Topics: Probability
Concepts: Kolmogorov’s axioms · Probability
People: Kolmogorov