Recent content by Smiling

Show that if E is a Borel measurable subset of R, then {(x,y)| x-y is in E} is also measurable in the product space of Borel measures... Also, if f is a measurable function, show that F(x,y)=f(x-y) is also measurable..

I know that I need to construct a measure space in which some subset of a measurable set of measure zero is not measurable. However, such measure space is not complete. It seems that there is a subset of the Cantor set that is not borel measurable...so, if you choose the Borel measure, then you...

Homework Statement Show that there exists measurable functions f_n defined on some measure subspace, st f_n-> f a.e. but such that f is not measurable. Homework Equations Converges a.e. means that converges everywhere except on a set of measure zero. The Attempt at a Solution Need...