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

(i)	$f : X \to [-\infty, \infty]$ is a D5600: Basic Borel function on $M$

$|f|$ is a function $X \to [0, \infty]$ so that this result is a consequence of R1237: Unsigned basic Borel function almost everywhere finite if integral is finite. $\square$