Let f and g be continuous positive functions defined on the interval [0,+∞), and let E⊂[0,+∞) be a set of positive measure. Prove that the range of the function defined on E×E by the relation F(x,y)=∫0xf(t)dt+∫0yg(t)dt has a nonvoid interior.
L. Losonczi functionintegrationreal analysisreal analysis unsolved