ThmDex – An index of mathematical definitions, results, and conjectures.
F8346
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that
(i) $E, F_0, F_1, F_2, \dots \in \mathcal{F}$ are each a D1109: Measurable set in $M$
(ii) $F_0, F_1, F_2, \ldots$ is a D5143: Set partition of $X$
Then \begin{equation} \mu(E) = \sum_{n \in \mathbb{N}} \mu(E \cap F_n) \end{equation}