# Definition:Random Variable/Definition 1

## Definition

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

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

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