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}