MULTIPLICATIVE INTEGRABILITY OF RIEMANN, LEBESGUE, DENJOY, PERRON AND KURZWEIL INTEGRALS

Abstract

In this paper we explore multiplicative integrability of these eponymous integrals: Riemann, Lebesgue, Denjoy, Perron, and Kurzweil. For an integrable function f, in each of these senses, we investigate and compare the conditions on a function g that makes the product fgintegrable. We conclude that all existing integrals do not preclude a more powerful integral yet to be developed.