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 \supseteq E_1 \supseteq E_2 \supseteq \cdots \end{equation} |
(iii) | \begin{equation} \exists \, n \in \mathbb{N} : \mu(E_n) < \infty \end{equation} |
Then
\begin{equation}
\lim_{n \to \infty} \mu(E_n)
= \mu \left( \lim_{n \to \infty} E_n \right)
\end{equation}