# Definition:Random Variable/Real-Valued/Definition 2

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.
Let $\map \BB \R$ be the Borel $\sigma$-algebra on $\R$.
Let $X$ be a random variable on $\struct {\Omega, \Sigma, \Pr}$ taking values in $\struct {\R, \map \BB \R}$.
Then we say that $X$ is a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.