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Kolmogorov's Axioms


Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that

1. For every Q_i in W, there is a real number Q(Q_i) (the Kolmogorov weight of Q_i) such that

 0<Q(Q_i)<1.

2. Q(Q_i)+Q(Q^__i)=1, where Q^__i denotes the complement of Q_i in W.

3. For the mutually exclusive subsets Q_1, Q_2, ... in W,

 Q(Q_1 union Q_2 union Q_3 union ...)=Q(Q_1)+Q(Q_2)+Q(Q_3)+....

See also

Probability Axioms

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Cite this as:

Weisstein, Eric W. "Kolmogorov's Axioms." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KolmogorovsAxioms.html

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