ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F10161 on D5103: Unsigned basic expectation
F10161
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to [0, \infty]$ is a D5101: Random unsigned basic number on $P$
The expectation of $X$ on $P$ is the D1699: Basic number \begin{equation} \mathbb{E}_{\mathbb{P}} X : = \int_{\Omega} X \, d \mathbb{P} \end{equation}