About the properties of Lebesgue measurable subsets

This is a doubt about Lebesgue measurable subsets

If I have two Lebesgue measurable subsets $E_1, E_2$ in $\mathbb{R}$, is the subset $E_1\times E_2$ Lebesgue measurable in $\mathbb{R}^2$?, If it is, How can I compute $|E_1\times E_2|_2$?

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Yes and $|E_1\times E_2|=|E_1||E_2|$ –  leo Nov 15 '12 at 6:12

Yes and it is more general, indeed it holds for $\mathbb{R}^n$. Here you can find the proof. For the second question I quote @leo.