A version of Hake's theorem for Kurzweil-Henstock integral in terms of variational measure

DOI10.1515/gmj-2019-2074zbMath1472.26002OpenAlexW2990625673WikidataQ126672402 ScholiaQ126672402MaRDI QIDQ2041372

Francesco Tulone, Valentin A. Skvortsov

Publication date: 19 July 2021

Published in: Georgian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/gmj-2019-2074

zbMATH Keywords

Kurzweil-Henstock integralvariational measuretopological measure spacederivation basisHake property

Mathematics Subject Classification ID

Denjoy and Perron integrals, other special integrals (26A39) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)

Related Items (5)

The \(L^r\)-variational integral ⋮ On descriptive characterizations of an integral recovering a function from its \(L^r\)-derivative ⋮ Henstock-Kurzweil integration on metric spaces revisited ⋮ Dunford-Henstock-Kurzweil and Dunford-McShane integrals of vector-valued functions defined on \(m\)-dimensional bounded sets ⋮ The 𝐻𝐾ᵣ-integral is not contained in the 𝑃ᵣ-integral

Cites Work

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• Henstock type integral in compact zero-dimensional metric space and quasi-measures representations
• Derivation bases on the real line. I
• Derivation bases on the real line. II
• Multidimensional dyadic Kurzweil-Henstock- and Perron-type integrals in the theory of Haar and Walsh series
• Differentiability and integrability in \(n\) dimensions with respect to \(\alpha\)-regular intervals
• The Hake's property for some integrals over multidimensional intervals
• Generalized Hake property for integrals of Henstock type
• The Hake's theorem on metric measure spaces
• The Hake's theorem and variational measures
• Improper Riemann integral and Henstock integral in \(\mathbb R^n\)
• Derivates of interval functions
• Henstock integration in the plane
• A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting

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