I have a homework question that I need a hint on...

Given f:R->R is absolutely continuous, I have shown that f maps sets of measure zero to sets of measure zero. I am yet to show that f maps measurable sets to measurable sets. I know that E is measurable iff it differs from a g-delta or an f-sigma by a set of measure zero, and it seems like that would be the way to go. In the previous problem I was able to use the fact that absolutely continuous functions are uniformly continuous, but I don't see how that applies here. I would appreciate any help anyone could provide. Thanks.

rogerpodger

P.S. I have to turn this in today, so if anyone is able, I would really appreciate their assistance. Thanks.