\begin{definition}[Definition:Random Variable/Continuous/Singular]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $X$ be a continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.
Let $\map \BB \R$ be the Borel $\sigma$-algebra on $\R$.
Let $\lambda$ be the Lebesgue measure on $\struct {\R, \map \BB \R}$. 
We say that $X$ is '''singular''' {{iff}}:
:there exists a $\lambda$-null set $B$ such that $\map \Pr {X \in B} = 1$.
\end{definition}