6533b830fe1ef96bd1297c51
RESEARCH PRODUCT
On Variational Measures Related to Some Bases
L. Di PiazzaB. BongiornoValentin A. Skvortsovsubject
differentiation basisPure mathematicsClass (set theory)Lebesgue measureBasis (linear algebra)Henstock integralApplied MathematicsMathematical analysisvariational measureInterval (mathematics)Absolute continuityInterval functionMeasure (mathematics)δ-variationPerron integralCalculus of variationsAnalysisMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-10-01 | Journal of Mathematical Analysis and Applications |