A General Perron Integral

Abstract

In this paper integrals are considered from the point of view of inverting differential operators. In order to do this it is necessary to introduce integrals more general than the Lebesgue integral and these integrals turn out to have other interesting properties (6, 7, 12). The integral introduced here is defined in the setting of axiomatic potential theory (2, 4). By defining it as generally as possible it not only includes the James P2-integral but inverts many of the standard second-order differential operators.