## Functiones et Approximatio Commentarii Mathematici

### Nets and sequences of Riemann and Riemann-type integrable functions with values in a Banach space

This article is in its final form and can be cited using the date of online publication and the DOI.

#### 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.

#### Article information

Source
Funct. Approx. Comment. Math., Advance publication (2019), 24 pages.

Dates
First available in Project Euclid: 9 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.facm/1573268429

Digital Object Identifier
doi:10.7169/facm/1789

#### Citation

Mondal, Pratikshan; Dey, Lakshmi Kanta; Ali, Sk. Jaker. Nets and sequences of Riemann and Riemann-type integrable functions with values in a Banach space. Funct. Approx. Comment. Math., advance publication, 9 November 2019. doi:10.7169/facm/1789. https://projecteuclid.org/euclid.facm/1573268429

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