Definition:Expectation/General Definition

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 $X$.