# Simple measure theory questions (inverse image)

1. May 4, 2012

### EV33

1. The problem statement, all variables and given/known data
I was wondering if we Let E be some set such that f-1(E) is measurable then so is f-1(E)c.

2. Relevant equations

If the set A is measurable then so is its compliment.

3. The attempt at a solution

I think the statement is true because f-1(E) is just a set and thus its compliment should also be measurable.