Definition:Random Variable/Continuous/Absolutely Continuous/Definition 2

Definition

Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.

Let $F_X$ be the cumulative distribution function of $X$.

We say that $X$ is an absolutely continuous random variable if and only if:

$F_X$ is absolutely continuous.