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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!!!

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    I'm sorry but I don't see how that helps at all :(2012-12-07
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    What do you know about measurability?2012-12-07
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    I have the definition of measurability of a function, which is what I gave above. Thats equivalent to showing that any interval's pre-image is open if you are in the Reals, and that the imaginary and complex parts are both measurable, for complex. I really don't know much else about it. Am I missing some key piece of knowledge?2012-12-07

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