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

Let $f : X \to [- \infty, \infty]$ be an D1921: Absolutely integrable function on $M$ such that

Let $f : X \to [- \infty, \infty]$ be an D1921: Absolutely integrable function on $M$ such that

(i) | $f =_{a.e.} 0$ |

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