(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove if $f$ is measurable on R and C is any closed set, f^{-1}(C) is measurable.

2. Relevant equations

Definition of measurability, closed sets etc.

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Prove f is measurable on any closed set

**Physics Forums | Science Articles, Homework Help, Discussion**