Definition:Random Variable/Continuous

Definition
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 $\struct {\Omega, \Sigma, \Pr}$ :


 * the cumulative distribution function of $X$ is continuous.