We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.
Musial P., Skvortsov V., Tulone F. (2022). THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 150(5), 2107-2114 [10.1090/proc/15788].
THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL
Tulone F.
2022-01-01
Abstract
We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.
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