We have deliberately omitted the measure with respect to which integration is performed, and measurability and boundedness hypotheses on the functions f and g. The reader can supply his own virtually at will. For example, ff could mean folf(x) dx, where dx is Lebegsue measure and f and g are assumed to be bounded and Lebesgue measurable. Replacing fP by f and gq by g, and writing 1/q = s, we must prove that