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 $|E_1\times E_2|_2$?
2026-05-14 08:42:21.1778748141
About the properties of Lebesgue measurable subsets
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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.