I know this is simple, but I just cannot get my head around. Can anyone explain the following?
if $\mathcal{C} \subset\mathcal{B}$ and $\sigma(\mathcal{C})=\mathcal{B}$, then $h^{-1}:\mathcal{C}\rightarrow\Sigma$, => h is $\Sigma$ measurable.
The proof in the book:
Let $\mathcal{E}$ be the class of elements B in $\mathcal{B}$ such that $h^{-1}(B)\in \Sigma$. Then $\mathcal{E}$ is a Sigma algebra. Then $\mathcal{C} \subset \mathcal{E}$.
So how does this prove it?