
measurable functions
Let f be a measurable function and g be a 11 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 ??
Any ideas please ?? Thanks

Re: measurable functions
Can you give information about the set on which $\displaystyle f$ and $\displaystyle g$ are defined?

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

Re: measurable functions
Do you mean Borel or Lebesgue measurable?

Re: measurable functions