ThmDex – An index of mathematical definitions, results, and conjectures.
F5092
Formulation 0
Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
Let $E_1, \dots, E_N \in \mathcal{F}$ each be a D1109: Measurable set in $M$ such that
(i) $E_1, \dots, E_N$ is a D1681: Disjoint set collection
Then \begin{equation} \mu \left( \bigcup_{n = 1}^N E_n \right) = \sum_{n = 1}^N \mu(E_n) \end{equation}