Definition:Random Variable/General Definition

Definition
Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space, and let $\left({X, \Sigma'}\right)$ be a measurable space.

A random variable (on $\left({\Omega, \Sigma, \Pr}\right)$) is a $\Sigma \, / \, \Sigma'$-measurable mapping $f: \Omega \to X$.

Also see

 * Definition:Discrete Random Variable
 * Definition:Continuous Random Variable