- #1
jinsing
- 30
- 0
Homework Statement
Prove if $f$ is measurable on R and C is any closed set, f^{-1}(C) is measurable.
Homework Equations
Definition of measurability, closed sets etc.
The Attempt at a Solution
I've been trying for a while to get this proof, but I seem to just end up stuck at the beginning. I think I want to point out that the complement of a closed set is an open set, and open sets are countable unions of open intervals, which are themselves measurable. But I'm not too sure, and I'd sure appreciate a gentle push in the right direction.
Thanks!