Editing Random variable (section)

===Almost sure equality===

Two random variables ''X'' and ''Y'' are ''equal [[almost surely]]'' (denoted <math>X \; \stackrel{\text{a.s.}}{=} \; Y</math>) if, and only if, the probability that they are different is [[Null set|zero]]:

:<math>\operatorname{P}(X \neq Y) = 0.</math>

For all practical purposes in probability theory, this notion of equivalence is as strong as actual equality. It is associated to the following distance:

:<math>d_\infty(X,Y)=\operatorname{ess} \sup_\omega|X(\omega)-Y(\omega)|,</math>

where "ess sup" represents the [[essential supremum]] in the sense of [[measure theory]].