A
probability measure on a
sample space S is a
function [math]\href{/cs2800/wiki/index.php/Pr}{Pr} : \href{/cs2800/wiki/index.php/2}{2}^\href{/cs2800/wiki/index.php/S}{S} \href{/cs2800/wiki/index.php/%E2%86%92}{→} \href{/cs2800/wiki/index.php?title=%E2%84%9D&action=edit&redlink=1}{ℝ}
[/math] satisfying the following three
properties:
- For all events [math]E
[/math], [math]\href{/cs2800/wiki/index.php/Pr}{Pr}(E) ≥ 0
[/math]
- [math]\href{/cs2800/wiki/index.php/Pr}{Pr}(S) = 1
[/math]
- For all disjoint events [math]E_1
[/math] and [math]E_2
[/math], [math]\href{/cs2800/wiki/index.php/Pr}{Pr}(E_1 \href{/cs2800/wiki/index.php/%E2%88%AA}{∪} E_2) = \href{/cs2800/wiki/index.php/Pr}{Pr}(E_1) + \href{/cs2800/wiki/index.php/Pr}{Pr}(E_2)
[/math]
These three
properties are referred to as the
Kolmogorov axioms.
