Definition:Random Variable/Continuous

Definition
Let $\mathcal E$ be an experiment with a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

A continuous random variable on $\left({\Omega, \Sigma, \Pr}\right)$ is a random variable $X: \Omega \to \R$ whose cumulative distribution function is continuous for all $x \in \R$.