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. Thank you for your time.