Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
| (i) | $X : \Omega \to \mathbb{R}^D$ is a D4383: Random euclidean real number on $P$ |
| (ii) | $E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each an D1716: Event in $P$ |
| (iii) | $E_0, E_1, E_2, \ldots$ is a D5143: Set partition of $\Omega$ |
Then
\begin{equation}
X
= \sum_{n = 0}^{\infty} X I_{E_n}
\end{equation}