\begin{definition}[Definition:Expectation/Continuous]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $X$ be a continuous random variable on $\struct {\Omega, \Sigma, \Pr}$.
Let $F_X$ be the cumulative distribution function of $X$.
The '''expectation of $X$''', written $\expect X$, is defined by: 
:$\ds \expect X = \int_\R x \rd F_X$
whenever: 
:$\ds \int_\R \size x \rd F_X < \infty$
with the integrals being taken as Riemann-Stieltjes integrals.
\end{definition}