Definition:Random Variable/General Definition

Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $\struct {X, \Sigma'}$ be a measurable space.

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

Also see

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