Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

Probability axioms

In Kolmogorov's probability theory, the probability P of some event E, denoted P(E), is usually defined such that P satisfies theKolmogorov axioms, named after the famous Russian mathematicianAndrey Kolmogorov, which are described below.

These assumptions can be summarised as: Let (Ω, FP) be ameasure space with P(Ω)=1. Then (Ω, FP) is a probability space, with sample space Ω, event space F and probability measure P.

An alternative approach to formalising probability, favoured by someBayesians, is given by Cox's theorem.

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