Let me define first: let us have $(\Omega_1,S_1,\mu_1)$ and $(\Omega_2,S_2,\mu_2)$ be measure spaces. If $E\subseteq \Omega_1\times\Omega_2$ then the $x$-slice of $E$ is defined by $E^x=\{y\in\Omega_2: (x,y)\in E\}$ we have the following assertions:
(1) If $E=A_1\times A_2$,$A_1\in B_1$ and $A_2\in B_2$, and if $x\in \Omega_1$ then $E^x\in B_2$.
(2) The function $x\rightarrow \mu_2(E^x) $ is $B_1$-measurable.
I have understood part (1) but in part (2) we are saying that $\mu_2(E^x)$ as a function of $x$ is $B_1$-measurable, I want to know how this function is defined, I mean the domain and codomain of this, I am totally confused here.