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probability axioms
In Kolmogorov's probability theory, the probability ''P'' of some event ''E'', denoted , is usually defined such that ''P'' satisfies the Kolmogorov axioms, named after the famous Russian mathematician Andrey Kolmogorov, which 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.
== Axioms ==
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