Tuesday, 9 February 2010

set theory - Non Lebesgue measurable subsets with "large" outer measure

Yes, I believe so - since subsets of a null set A (i.e., m(A)=0) are not necessarily measurable, but will obviously still have outer measure 0, given any measurable set E you "should" (i.e., I think so, but not sure) be able to find a non-measurable subset S of a null set A inside E, remove S, and since m(E)=m(ES)+m(S) and m(S) isn't anything, we must have that m(ES) isn't anything, while we still have mast(E)=mast(ES)+mast(S)=mast(ES).

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