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Show that for a borel set A, we have that u(AE)=u(A), where AE is the intersection.

we have that u(A)=u(AE)+u(A\E) so we only have to prove u(A/E)=0

u(A/E)=inf(u(M):M is open and A\E is a subset of M)

A\E is disjoint with E but unfortunately this does not imply M is disjoint with E .