i've proven that for countable $A$ this is absolutely true, but i don't think this statement is true for uncountable A. I've tried to make a function with the cantor set but i still haven't found a real good counterexample.
help would be appreciated!
Kees
On
The result is certainly true for absolutely continuous functions and diffeomorphisms. The classical counter-example is the Cantor function, as already pointed by Robert Israel.
It's not even true for continuous functions. Try the Cantor function.