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) | $E \in \mathcal{F}$ is an D1716: Event in $P$ |
| (iv) | \begin{equation} \mathbb{P}(E) = 0 \end{equation} |
Then
\begin{equation}
\mathbb{E}(Z I_E)
= 0
\end{equation}