Definition:Measurable Function/Positive
< Definition:Measurable Function(Redirected from Definition:Positive Measurable Function)
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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.
Also see
- Results about measurable functions can be found here.