(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!

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# Homework Help: Prove f is measurable on any closed set

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