\begin{definition}[Definition:Random Variable/Continuous/Absolutely Continuous/Definition 1]
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 $\map \BB \R$ be the Borel $\sigma$-algebra of $\R$.
Let $\lambda$ be the Lebesgue measure on $\struct {\R, \map \BB \R}$. 
We say that $X$ is an '''absolutely continuous random variable''' {{iff}}:
:$P_X$ is absolutely continuous with respect to $\lambda$.
\end{definition}