Influence of the Choice of the Class of Gauge Functions on the Properties of the Henstock–Kurzweil Integral

Properties of the Henstock–Kurzweil integral are considered under restrictions imposed on a gauge function. A proof of the assertion on relationships between the classes of integrable functions and the classes of gauge functions is presented for several particular cases.

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Published in:	Moscow University mathematics bulletin Vol. 76; no. 2; pp. 65 - 68
Main Author:	Kopylov, S. N.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-03-2021 Springer Nature B.V
Subjects:	Analysis Integrals Mathematical functions Mathematics Mathematics and Statistics integration theory Henstock–Kurzweil integral real analysis
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Abstract	Properties of the Henstock–Kurzweil integral are considered under restrictions imposed on a gauge function. A proof of the assertion on relationships between the classes of integrable functions and the classes of gauge functions is presented for several particular cases.
AbstractList	Properties of the Henstock–Kurzweil integral are considered under restrictions imposed on a gauge function. A proof of the assertion on relationships between the classes of integrable functions and the classes of gauge functions is presented for several particular cases.
Author	Kopylov, S. N.
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References	BurkF. E.A Garden of Integrals2007WashingtonThe Math. Assoc. of America10.7135/UPO9781614442097 PfefferW. F.A note on the generalized Riemann integralProc. Am. Math. Soc.19881031161116695500010.1090/S0002-9939-1988-0955000-40656.26010 LukashenkoT. P.SkvortsovV. A.SolodovA. P.Generalized Integrals2011MoscowLibrokom ForanJ.MeinershagenS.Some answers to a question of P. BullenReal Anal Exch.19871326527792373110.2307/44151877 BullenP.Queries 178Real Anal. Exch.19861239310.2307/44151807 BuczolichZ.Nearly upper semicontinuous gauge functions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^{n}$$\end{document}Real Anal. Exch.19871343644094357010.2307/441518940656.26008 F. E. Burk (7039_CR6) 2007 P. Bullen (7039_CR2) 1986; 12 J. Foran (7039_CR3) 1987; 13 W. F. Pfeffer (7039_CR4) 1988; 103 Z. Buczolich (7039_CR5) 1987; 13 T. P. Lukashenko (7039_CR1) 2011
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Title	Influence of the Choice of the Class of Gauge Functions on the Properties of the Henstock–Kurzweil Integral
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