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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2024, Number 1, Pages 20–31
DOI: https://doi.org/10.55959/vmumm4585 (Mi vmumm4585) 		 
Mathematics

Kolmogorov's ideas on the theory of integral in modern research

T. P. Lukashenkoab, V. A. Skvortsovab, A. P. Solodovab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow
b Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.55959/vmumm4585
Abstract: Generalizations of construction of Kolmogorov integral to the case of Banach space-valued functions are considered. We demonstrate how the Kolmogorov ideas on integration theory, in particular the notion of differential equivalence, have been developed in the theory of the Henstock–Kurzweil integral. In this connection, a variational version of a Henstock type integral with respect to a rather general derivation basis is studied. An example of an application of this integral in harmonic analysis is given. Some results related to Kolmogorov $A$-integral are also considered.
Key words: Kolmogorov integral, Riemann sums, differential basis, differential equivalence, Henstock–Kurzweil integral, $A$-integral.
Funding agency Grant number
Foundation for the Advancement of Theoretical Physics and Mathematics BASIS
Received: 31.05.2023
English version:
Moscow University Mathematics Bulletin, 2024, Volume 79, Issue 1, Pages 22–33
DOI: https://doi.org/10.3103/S0027132224700037
Bibliographic databases:
Document Type: Article
UDC: 517.518.126
Language: Russian
Citation: T. P. Lukashenko, V. A. Skvortsov, A. P. Solodov, “Kolmogorov's ideas on the theory of integral in modern research”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 1, 20–31; Moscow University Mathematics Bulletin, 79:1 (2024), 22–33
Citation in format AMSBIB
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\by T.~P.~Lukashenko, V.~A.~Skvortsov, A.~P.~Solodov
\paper Kolmogorov's ideas on the theory of integral in modern research
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2024
\issue 1
\pages 20--31
\mathnet{http://mi.mathnet.ru/vmumm4585}
\crossref{https://doi.org/10.55959/vmumm4585}
\elib{https://elibrary.ru/item.asp?id=62487630}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2024
\vol 79
\issue 1
\pages 22--33
\crossref{https://doi.org/10.3103/S0027132224700037}
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