Definition:Measurable Function/Extended Real-Valued Function/Definition 2

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

Let $\map \BB {\overline \R}$ be the Borel $\sigma$-algebra on the extended real number space.

An extended real-valued function $f: X \to \overline \R$ is said to be ($\Sigma$-)measurable $f$ is $\Sigma \, / \, \map \BB {\overline \R}$-measurable.