Problems(1)
Let f(x,y) be a continuous function on the square S={(x,y):0≤x≤1,0≤y≤1}. For each point (a,b) in the interior of S, let S(a,b) be the largest square that is contained in S, is centered at (a,b), and has sides parallel to those of S. If the double integral ∫∫f(x,y)dxdy is zero when taken over each square S(a,b), must f(x,y) be identically zero on S? college contests