A new descriptive characterization of the HKr-integral and its inclusion in Burkill's integrals

Abstract

We introduce a new class of functions, ACGr⁎, and compare it to the class of ACGr-functions which had been previously introduced by Musial and Sagher to characterize their Henstock–Kurzweil-type integral, the HKr-integral. We show that these two classes coincide and thereby we obtain a new descriptive characterization of the class of HKr-integrable functions. We then compare the HKr-integral with Burkill's CP-integral and obtain a de la Vallée Poussin-type theorem for the HKr-integral.