ThmDex – An index of mathematical definitions, results, and conjectures.
F8897
Formulation 0
Let $M = (X, \mathcal{F}, \mathbb{\mu})$ be a D1158: Measure space such that
(i) $E_0, E_1, E_2, \ldots \in \mathcal{F}$ are each a D1109: Measurable set in $M$
(ii) \begin{equation} E_0 \subseteq E_1 \subseteq E_2 \subseteq \cdots \end{equation}
Then \begin{equation} \lim_{n \to \infty} \mu(E_n) = \mu \left( \bigcup_{n \in \mathbb{N}} E_n \right) \end{equation}