ThmDex – An index of mathematical definitions, results, and conjectures.
F13428
Formulation 1
Let $X, Y \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \exists \, y \in \mathbb{R} : \forall \, \omega \in \Omega : Y(\omega) = y \end{equation}
Then \begin{equation} \mathbb{E} (X \mid Y) \overset{a.s.}{=} \mathbb{E} X \end{equation}