# Real Analysis! HELP!

1. Nov 6, 2008

### Smiling

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Converges a.e. means that converges everywhere except on a set of measure zero.

3. The attempt at a solution
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 compelte.

2. Nov 7, 2008

### Smiling

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 know it is not complete and that m(Cantor set)=0...
I am not sure how to choose the function though...maybe choose the Cantor function?