On variational measures related to some bases

DOI10.1006/JMAA.2000.6983zbMath0966.26006OpenAlexW1977253232MaRDI QIDQ1589711

Valentin A. Skvortsov, Benedetto Bongiorno, Luisa Di Piazza

Publication date: 19 March 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6983

zbMATH Keywords

Henstock integralPerron integralvariational measuredifferentiation basis

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Denjoy and Perron integrals, other special integrals (26A39)

Related Items (6)

On some variational measures related to the wide Denjoy integral and its counterparts ⋮ The Ward property for a \(\mathcal P\)-adic basis and the \(\mathcal P\)-adic integral. ⋮ On the Denjoy-Luzin definitions of the function classes ACG ACG\(^*\), VBG, and VBG\(^*\) ⋮ Variational measures related to local systems and the Ward property of $$\mathcal{P}$$ -adic path bases ⋮ On dyadic integrals and some other integrals associated with local systems ⋮ On the minimal solution of the problem of primitives

Cites Work

• The inversion of approximate and dyadic derivatives using an extension of the Henstock integral
• Une théorie de Denjoy des martingales dyadiques. (A Denjoy theory of dyadic martingales)
• Differentiation of integrals in \(\mathbb{R}^n\)
• On absolute continuity
• Infinite variation and derivatives in \(R^m\)
• Variations and variational measures in integration theory and some applications
• Variational measure and sufficient differentiability condition of additive interval function
• Symmetric integrals do not have the Marcinkiewicz property
• A new full descriptive characterization of Denjoy-Perron integral
• On continuous major and minor functions for the \(n\)-dimensional Perron integral
• Notes on the approximately continuous Henstock integral
• The essential variation of a function and some convergence theorems
• Derivates of interval functions
• Variational Measures in the Theory of the Integration in ℝ m
• Henstock integration in the plane
• A Full Descriptive Definition of the Gage Integral
• Some properties of variational measures
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