The Lr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{r}$$\end{document}-Variational Integral

被引：0
作者：
Francesco Tulone
Paul Musial
机构：
[1] University of Palermo,
[2] Chicago State University,undefined
来源：
Mediterranean Journal of Mathematics | 2022年 / 19卷 / 3期
关键词：
-Variational Integral; Integral; Non-absolute integral; 26A39; 28C99;
D O I：
10.1007/s00009-021-01962-8
中图分类号：
学科分类号：
摘要：
We define the Lr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^r$$\end{document}-variational integral and we prove that it is equivalent to the HKr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$HK_r$$\end{document}-integral defined in 2004 by P. Musial and Y. Sagher in the Studia Mathematica paper TheLr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{r}$$\end{document}-Henstock–Kurzweil integral. We prove also the continuity of Lr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^r$$\end{document}-variation function.
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