A little question about the basics of Lebesgue integration. There is a theorem: if functions f and g are L-integrable then the function f+g is also L-integrable. This may be dumb, but I wish to know about the reciprocal lemma. Let h be a L-integrable function and f and g be functions such that h(x) = f(x) + g(x). Are f and g L-integrable? I suppose it is truth because I cant see how, being f a not L-integrable function, h could yet be a L-integrable one. But I cant' see the proof. Does someone got a minute to help? Thanks.