Given a (Lebesgue) measurable set $A$ and a nonmeasurable set $B$, when is $A \cap B$ measurable? Nonmeasurable?
I think I know a case where the intersection turns out to be nonmeasurable (it involves the Cantor-Lebesgue function). I assume there are trivial cases (e.g. intersecting two disjoint sets), but I'm curious about more general results.
Also, what about the union of measurable and nonmeasurable sets?
I apologize in advance if this is a duplicate; I looked around MSE for a bit so to my knowledge it is not.