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

(i)	$E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$
(ii)	$E_0, E_1, E_2, \ldots $ is a D83: Proper set partition of $\Omega$
(iii)	\begin{equation} \mathbb{P}(E_0), \mathbb{P}(E_1), \mathbb{P}(E_2), \ldots > 0 \end{equation}
(iv)	$\mathcal{G} := \sigma \langle E_0, E_1, E_2, \ldots \rangle$ is a D318: Generated sigma-algebra on $\Omega$ with generators $E_0, E_1, E_2, \ldots$
(v)	$X : \Omega \to \mathbb{R}$ is an D3161: Random real number on $P$
(vi)	\begin{equation} \mathbb{E} |X| < \infty \end{equation}

Then \begin{equation} \forall \, n \in \mathbb{N} \text{ and } \omega \in \Omega \left( \omega \in E_n \quad \implies \quad \mathbb{E}(X \mid \mathcal{G}) (\omega) \overset{a.s.}{=} \frac{\mathbb{E} (X I_{E_n})}{\mathbb{P}(E_n)} \right) \end{equation}