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On Variational Measures Related to Some Bases |
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| Authors: | B Bongiorno L Di Piazza V A Skvortsov |
| Institution: | a Department of Mathematics, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy;Department of Mathematics, Moscow State University, Moscow, 119899, Russiaf1;c Instytut Matematyki, WSP, 85-065, Bydgoszcz, Poland |
| Abstract: | We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis. |
| Keywords: | variational measure δ -variation differentiation basis Henstock integral Perron integral |
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