Conditions for a map to be a measurable map

This page is intended to be a list of different conditions for a function to be a measurable map

Conditions

• A map, $f:(A,\mathcal{A})\rightarrow(F,\mathcal{F})$, is $\mathcal{A}/\mathcal{F}$ measurable iff for some generator $\mathcal{F}_0$ of $\mathcal{F}$ we have $\forall S\in\mathcal{F}_0[f^{-1}(S)\in\mathcal{A}]$