Changing the order of integration

Abstract

Repeated improper Riemann integrals arise in a variety of contexts, and the validity of changing the order of integration is often in question. Fubini's theorem ensures the equality of two repeated Lebesgue integrals when one of them is absolutely convergent. For many years I have assumed that an analogous test is applicable to repeated improper R-integrals, since they will be absolutely convergent and therefore in agreement with the corresponding L-integrals.