Definition:Space of Measurable Functions/Extended Real-Valued

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Definition

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


Then the space of $\Sigma$-measurable, extended real-valued functions $\map {\MM_{\overline \R}} {X, \Sigma}$ is the set of all $\Sigma$-measurable, extended real-valued functions.

That is:

$\map {\MM_{\overline \R}} {X, \Sigma} := \set {f: X \to \overline \R: f \text{ is $\Sigma$-measurable} }$


Also see


Sources