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

(i)	$Z : \Omega \to \mathbb{C}$ is a D4877: Random complex number on $P$
(ii)	\begin{equation} \mathbb{E} |Z| < \infty \end{equation}
(iii)	$\xi : \Omega \to \Xi$ is a D202: Random variable on $P$
(iv)	$\{ \xi \in S_0 \}, \{ \xi \in S_1 \}, \{ \xi \in S_2 \}, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$
(v)	$\{ \xi \in S_0 \}, \{ \xi \in S_1 \}, \{ \xi \in S_2 \}, \ldots$ is a D83: Proper set partition of $\Omega$
(vi)	\begin{equation} \forall \, n \in \mathbb{N} : \mathbb{P}(\xi \in S_n) > 0 \end{equation}

Then \begin{equation} \mathbb{E}(Z) = \sum_{n = 0}^{\infty} \mathbb{E}(Z \mid \xi \in S_n) \mathbb{P}(\xi \in S_n) \end{equation}