Definition:Space of Measurable Functions/Positive/Real-Valued

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

Then the space of $\Sigma$-measurable, positive real-valued functions $\map {\MM^+} \Sigma$ is the subset of $\map {\MM} \Sigma$ consisting of the positive $\Sigma$-measurable functions in $\map \MM \Sigma$.

That is:


 * $\map {\MM^+} \Sigma := \set {f: X \to \R: f \text{ is positive $\Sigma$-measurable} }$

Also see

 * Space of Real-Valued Measurable Functions