Kolmogorov Axioms


Kolmogorov axioms or probability axioms were introduced by Soviet mathematician Andrey Kolmogorov(April 25, 1903- October 20, 1987). 

All the theorems in probability theory are derived from the axioms.


Given a sample space S and a σ-algebra F, a probability function P must satisfy the following three properties:

    1. For any element A of σ-algebra F, P(A) ≧ 0.

    2. P(S) = 1.

    3. If    of σ-algebra F are pairwise disjoint  .

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