Definition:Measurable Mapping

Definition
Let $\struct {X, \Sigma}$ and $\struct {X', \Sigma'}$ be measurable spaces.

A mapping $f: X \to X'$ is said to be $\Sigma \, / \, \Sigma'$-measurable :


 * $\forall E' \in \Sigma': \map {f^{-1} } {E'} \in \Sigma$

That is, the preimage of every measurable set under $f$ is again measurable.

Also known as
When no danger of ambiguity arises, a $\Sigma \, / \, \Sigma'$-measurable mapping $f$ may simply be called measurable.