Measurable map

Definition

Let $(X,\mathcal{A})$ and $(X',\mathcal{A}')$ be measurable spaces

Then a map $$T:X\rightarrow X'$$ is called $$\mathcal{A}/\mathcal{A}'$$ -measurable if

$$T^{-1}(A')\in\mathcal{A},\ \forall A'\in\mathcal{A}'$$