Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that

(i)	$f_0, f_1, f_2, \ldots : X \to [0, \infty]$ are each a D5600: Basic Borel function on $M$

Then \begin{equation} \int_X \lim_{N \to \infty} \sum_{n = 0}^N f_n \, d \mu = \lim_{N \to \infty} \sum_{n = 0}^N \int_X f_n \, d \mu \end{equation}