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 $M$ |
Then $|f| \overset{a.e.}{<} \infty$ if and only if
(1) | \begin{equation} f^+ \overset{a.e.}{<} \infty \end{equation} |
(2) | \begin{equation} f^- \overset{a.e.}{<} \infty \end{equation} |