# Math Help - measurable functions

1. ## measurable functions

Let f be a measurable function and g be a 1-1 function from R to R which has a Lipschitz inverse.

Show that the composition fog is measurable

My idea was to take a set (a,00) , then f^-1(a,00) is measurable call this set C , but i need to prove that g^-1(C) is measurable
Since g^-1 is Lipschitz then it is continuous. Let g^-1 = h , so how can I prove that h(C) is measurable provided that h is Lipschitz, hence continuous ??

2. ## Re: measurable functions

Can you give information about the set on which $f$ and $g$ are defined?

3. ## Re: measurable functions

It is R the real numbers. I think I mentioned that in the question. Thank you !

4. ## Re: measurable functions

Do you mean Borel or Lebesgue measurable?

5. ## Re: measurable functions

Lebesgue measurable