Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$\mathcal{G} \subseteq \mathcal{F}$ is a D470: Subsigma-algebra of $\mathcal{F}$ on $\Omega$
(ii)	$X : \Omega \to \Xi$ is an D3066: Absolutely integrable random number on $P$
(iii)	$\sigma_{\text{pullback}} \langle X \rangle, \mathcal{G}$ is an D471: Independent collection of sigma-algebras in $P$

Then $$\begin{equation} \mathbb{E}(X \mid \mathcal{G}) \overset{a.s.}{=} \mathbb{E}(X) \end{equation}$$