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

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

Let $\map \BB \R$ be the Borel $\sigma$-algebra on $\R$.

A real-valued function $f: X \to \R$ is said to be ($\Sigma$-)measurable $f$ is $\Sigma \, / \, \map \BB \R$-measurable.