Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space.
Let $f, g: X \to [0, \infty]$ each be a D313: Measurable function on $M$.
Let $\alpha, \beta \in [0, \infty)$ each be an D4767: Unsigned real number.

Then \begin{equation} \int_X (\alpha f + \beta g) \, d \mu = \alpha \int_X f \, d \mu + \beta \int_X g \, d \mu \end{equation}