Let $f : X \to \mathbb{R}^D$ be a D4363: Euclidean real function such that
(i) | $E_0, E_1, E_2, \ldots \subseteq X$ are each a D78: Subset of $X$ |
(ii) | $E_0, E_1, E_2, \ldots$ is a D5143: Set partition of $X$ |
Then
\begin{equation}
f =
\sum_{n = 0}^{\infty} f I_{E_n}
\end{equation}