Lebesgue measurable but not Borel measurable I'm trying to find a set which is Lebesgue measurable but not Borel measurable.
So I was thinking of taking a Lebesgue set of measure zero and intersecting it with something so that the result is not Borel measurable.
Is this a good approach? Can someone give a hint what set I would take (so please no full answers, I want to find it myself in the end ;-))
Also, I seem to remember that to construct a non-Lebesgue measurable set one needs to use the axiom of choice. Is this also the case for non-Borel measurable sets?

There is some good stuff here:
https://mathoverflow.net/questions/32720/non-borel-sets-without-axiom-of-choice
