\begin{definition}[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 $\struct {\Omega, \Sigma, \Pr}$. 
Category:Definitions/Random Variables
\end{definition}