Let (X, E, u) be a measure space with u a non-negative measure. Suppose that
1. f : X -> R is measurable
2. f (x) >= 0 a.e. with respect to u.
3. integral (over X) f du = 0
Prove that f (x) = 0 a.e. with respect to u.
note: E = Capital Sigma
u = lowercase mu