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...