ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4566 on D41: Indicator function
Countable indicator partition of a complex function
Formulation 0
Let $f : X \to \mathbb{C}$ be a D4881: Complex 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}