Definition:Space of Measurable Functions/Extended Real-Valued
< Definition:Space of Measurable Functions(Redirected from Definition:Space of Extended Real-Valued Measurable Functions)
Jump to navigation
Jump to search
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
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $8.4$