\begin{definition}[Definition:Expectation/General Definition]
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space. 
Let $X$ be an integrable real-valued random variable on $\struct {\Omega, \Sigma, \Pr}$.
The '''expectation of $X$''', written $\expect X$, is defined by: 
:$\ds \expect X = \int X \rd \Pr$
where the integral sign denotes the $\Pr$-integral of $X$.
\end{definition}