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.
Musial P., Skvortsov V., Sworowski P., Tulone F. (2025). A new descriptive characterization of the HKr-integral and its inclusion in Burkill's integrals. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 542(1) [10.1016/j.jmaa.2024.128758].
A new descriptive characterization of the HKr-integral and its inclusion in Burkill's integrals
Tulone F.
2025-02-01
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.
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