Probability axioms

The Kolmogorov axioms are a fundamental part of Andrey Kolmogorov's probability theory.In it, the probability P of some event E, denoted P ( E ) {displaystyle P(E)} , is usually defined as to satisfy these axioms.The axioms are described below. The Kolmogorov axioms are a fundamental part of Andrey Kolmogorov's probability theory.In it, the probability P of some event E, denoted P ( E ) {displaystyle P(E)} , is usually defined as to satisfy these axioms.The axioms are described below. These assumptions can be summarised as follows: Let (Ω, F, P) be a measure space with P(Ω) = 1. Then (Ω, F, P) is a probability space, with sample space Ω, event space F and probability measure P. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem.