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

(i)	$f : X \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$
(ii)	$E \in \mathcal{F}$ is a D1109: Measurable set in $M$
(iii)	\begin{equation} \mu(E) = 0 \end{equation}

Then \begin{equation} \int_E f \, d \mu = 0 \end{equation}