1. The problem statement, all variables and given/known data If D is open, and if f is continuous, bounded, and obeys f(p)>or=0 for all p in D, then the double integral over D of f is equal to 0 implies f(p) = 0 for all p. 2. Relevant equations Hint: There is a neighborhood where f(p)>or=d. 3. The attempt at a solution The integral is equal to the sum of f(p)*A(Rij) for some Rij partition of f(x). Since Rij > 0, for the whole thing to be 0, f(p) has to be 0. Not really sure how to start my proof. f is continuous and m<or= f(p) <or= M so mA(D) <or= double integral <or= MA(D) since the double integral is = 0, mA(D) <or= 0 <or= MA(D) which means m=M=0 and f(p) = 0 for all p. Is this correct?