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)	$X : \Omega \to \mathbb{R}$ is a D3161: Random real number on $P$
(iii)	\begin{equation} \mathbb{E} |X| < \infty \end{equation}
(iv)	\begin{equation} \sigma_{\text{pullback}} \langle X \rangle \subseteq \mathcal{G} \end{equation}

Then \begin{equation} \mathbb{P} \left( \mathbb{E}(X \mid \mathcal{G}) = X \right) = 1 \end{equation}