18 мая 2015 г. · If A is a set of positive measure, then there exists a subset D of A that is non measurable. I am not sure how to prove it. I have read the ...

1 янв. 2017 г. · We know that the Lebesgue measure obtained via the usual Caratheodory extension is complete. As such, the subset of every null set is null.

11 апр. 2015 г. · Theorem: If A⊂R and every subset of A is Lebesgue measurable then m(A)=0 Corollary: Every set of positive measure has non-measurable subsets.

30 апр. 2023 г. · A is a set with positive outer measure which does not contain any measurable subset with positive measure.

3 окт. 2012 г. · If A is measurable and has positive outer measure, it has positive measure, so it has a subset B which isn't measurable by the theorem.

5 нояб. 2013 г. · Any set A⊆R that is not of Lebesgue measure zero has a subset that is not measurable. To see this, note first that if A itself is nonmeasurable, ...

22 сент. 2022 г. · I need to prove that if A⊆Rn is measurable with positive measure, then it contains a non-measurable set. I produced a proof but I think it is ...

5 дек. 2011 г. · Moreover, every nonmeasurable set A contains a nonmeasurable subset B such that every measurable subset of B has measure zero. – bof. Commented ...

23 дек. 2018 г. · Since E has positive measure it contains a nonmeasurable set V, and every measurable subset of V is null, but I could not show V contains ...

17 апр. 2011 г. · Every nonmeasurable set contains nonmeasurable subsets with no measurable subsets of positive measure.