Definition:Measurable Function/Positive

Definition

Let $\struct {X, \Sigma}$ be a measurable space.

Let $S \in \set {\R, \overline \R}$.

Let $f : X \to S$ be a $\Sigma$-measurable function.

We say that $f$ is a positive $\Sigma$-measurable function if and only if:

$f \ge 0$

where $\ge$ denotes pointwise inequality.