Definition:Random Variable/Continuous/Absolutely Continuous

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

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

Let $P_X$ be the probability distribution of $X$.

Let $\lambda$ be the Lebesgue measure on $\R$.

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


 * $P_X$ is absolutely continuous with respect to $\lambda$.

Also see

 * Absolutely Continuous Random Variable is Continuous