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June 2020 Nets and sequences of Riemann and Riemann-type integrable functions with values in a Banach space
Sk. Jaker Ali, Lakshmi Kanta Dey, Pratikshan Mondal
Funct. Approx. Comment. Math. 62(2): 203-226 (June 2020). DOI: 10.7169/facm/1789

Abstract

In this article, we discuss several aspects of convergence theorems for nets and sequences of Riemann and Riemann-type integrable functions defined on a closed bounded interval in $\mathbb{R}$ with values in a Banach space. We introduce the notions of Riemann $\Delta$-Cauchy nets of functions with its analogous variants and derive some correlations between such kind of nets of functions and equi-Riemann integrability. Moreover, we establish equi-integrability of the pointwise closure of different types of equi-integrable collections of functions. Finally, several related results, e.g., relative compactness of equi-integrable collections of functions with respect to different topologies are studied.

Citation

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Sk. Jaker Ali. Lakshmi Kanta Dey. Pratikshan Mondal. "Nets and sequences of Riemann and Riemann-type integrable functions with values in a Banach space." Funct. Approx. Comment. Math. 62 (2) 203 - 226, June 2020. https://doi.org/10.7169/facm/1789

Information

Published: June 2020
First available in Project Euclid: 9 November 2019

zbMATH: 07225510
MathSciNet: MR4113986
Digital Object Identifier: 10.7169/facm/1789

Subjects:
Primary: 28B05, 40A30
Secondary: 46G10

Rights: Copyright © 2020 Adam Mickiewicz University

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Vol.62 • No. 2 • June 2020
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