\begin{definition}[Definition:Measurable Mapping]
Let $\struct {X, \Sigma}$ and $\struct {X', \Sigma'}$ be measurable spaces.
A mapping $f: X \to X'$ is said to be '''$\Sigma \, / \, \Sigma'$-measurable''' {{iff}}:
:$\forall E' \in \Sigma': \map {f^{-1} } {E'} \in \Sigma$
That is, {{iff}} the preimage of every measurable set under $f$ is again measurable.
\end{definition}