Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
Let $f_1, \ldots, f_N : X \to [0, \infty]$ each be a D313: Measurable function on $M$.

Then \begin{equation} \int_X \left( \sum_{n = 1}^N f_n \right) \, d \mu = \sum_{n = 1}^N \left( \int_X f_n \, d \mu \right) \end{equation}