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
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
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