Abstract
The note is related to a recently published paper J.M. Park, J. J. Oh, C.-G. Park, D.H. Lee: The AP-Denjoy and AP-Henstock integrals. Czech. Math. J. 57 (2007), 689–696, which concerns a descriptive characterization of the approximate Kurzweil-Henstock integral. We bring to attention known results which are stronger than those contained in the aforementioned work. We show that some of them can be formulated in terms of a derivation basis defined by a local system of which the approximate basis is known to be a particular case. We also consider the relation between the _-finiteness of variational measure generated by a function and the classical notion of the generalized bounded variation.
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Supported by RFFI-11-01-00321 and by NSh-3252.2010.1.
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Skvortsov, V.A., Sworowski, P. The AP-Denjoy and AP-Henstock integrals revisited. Czech Math J 62, 581–591 (2012). https://doi.org/10.1007/s10587-012-0050-5
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DOI: https://doi.org/10.1007/s10587-012-0050-5