\begin{definition}[Definition:Random Variable/Continuous]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $X$ be a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.
We say that $X$ is a '''continuous random variable''' on $\struct {\Omega, \Sigma, \Pr}$ {{iff}}:
:the cumulative distribution function of $X$ is continuous.
\end{definition}