Definition:Measurable Function/Real-Valued Function/Definition 2
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Definition
Let $\struct {X, \Sigma}$ be a measurable space.
Let $E \in \Sigma$.
Let $\Sigma_E$ be the trace $\sigma$-algebra of $E$ in $\Sigma$.
Let $\map \BB \R$ be the Borel $\sigma$-algebra on $\R$.
Let $f : E \to \R$ be a real-valued function.
We say that $f$ is ($\Sigma$-)measurable if and only if:
Sources
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 8$