ThmDex – An index of mathematical definitions, results, and conjectures.
F10845
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $X : \Omega \to \mathbb{R}$ is a D3161: Random real number on $P$
(ii) \begin{equation} \mathbb{E} |X| < \infty \end{equation}
Then \begin{equation} \mathbb{E}(X \mid \{ \emptyset, \Omega \}) \overset{a.s.}{=} \mathbb{E} X \end{equation}