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Richardtb

Richardtb

Answered question

2022-05-23

Assume E R p , F R q and E × F is measurable set in R p + q .
Is it possible for any of E , F is not measurable in their own space?

Answer & Explanation

bgu999dq

bgu999dq

Beginner2022-05-24Added 9 answers

So, basically, we are trying to figure out whether every projection of a measurable set is measurable. Consider the interval [0,1], there is a set E that is not measurable in [0,1]. Now consider E × { 0 } in R 2 , this set is a null set, hence measurable. Here, I am assuming we are working with the Lebesgue measure on the Lebesgue algebra (so, every null set is measurable).

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