Consider the following functions:
Modified Dirichlet Function
f(x) = 1/n if x=m/n of lowest forms, and f(x) = 0 if x is irrational
find an integrable function g(x) such that the composition of g and f is NOT integrable
The Attempt at a Solution
Let g(x) = nx for all n in N (natural numbers)
h(x) = g(f(x)) = n(1/n) = 1 if x is rational, and h(x) = g(f(x))= n(0) = 0 if x is irrational
My g(x) is apparently incorrect. Can anyone tell me why?
I appreciate your help,
note: I already know the correct answer, I just need to confirm that the g(x) I came up with is incorrect.