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

2024; Elsevier BV; Volume: 542; Issue: 1 Linguagem: Inglês

10.1016/j.jmaa.2024.128758

1096-0813

Paul Musial, В. А. Скворцов, Piotr Sworowski, Francesco Tulone,

Mathematical functions and polynomials

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.