I was hoping someone can point me in the right direction for the proof of this question. I have some idea of whats going on, but I need a little more. Anyway, here is the statement.
We are given that $a$ is an $R$-measurable function on $\Gamma$ and that $b$ is an $S$-measurable function on $\Lambda$. Then we are given $f(x,y)=a(x)b(y)$, and the goal is to prove that $f$ is $R \times S$ measurable.
I'm a little new to this product measure stuff, but I know that to prove that $f$ is $R \times S$ measurable I need to show that $f^{-1}(O) \in R \times S$ for some arbitrary open set $O$ (in the complex numbers). I just don't see how one is able to show that. Do I have to use sections of the sets (or of the functions)?
Thanks!!!