Suppose there exists such that then since is continous and open there exists an such that for all we have and since is Jordan measurable a contradiction.
Suppose there exists such that then since is continous and open there exists an such that for all we have and since is Jordan measurable a contradiction.
But what if f(y) can be both positive or negative?
If it's negative use the exact same argument with the inequalities reversed, and note that continuity is crucial since it lets us pick a ball around y where f is positive (or negative).