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September 2020 Nets and sequences of $p$-Bochner, $p$-Dunford and $p$-Pettis integrable functions with values in a Banach space
Sk. Jaker Ali, Lakshmi Kanta Dey, Pratikshan Mondal
Funct. Approx. Comment. Math. 63(1): 43-65 (September 2020). DOI: 10.7169/facm/1818

Abstract

In this paper, we study convergence of nets and sequences of $p$-Bochner, $p$-Dunford and $p$-Pettis integrable functions, $p \in [1, \infty)$, defined on a finite measure space with values in a real Banach space. Applying Hölder's inequality, we study some properties of these functions and convergence of their nets and sequences. We introduce the idea of $\delta$-Cauchy nets in terms of which we establish convergence theorems for nets of above types of functions. We see that $\delta$-Cauchyness of a net plays the similar role as uniform integrability does in case of sequences.

Citation

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Sk. Jaker Ali. Lakshmi Kanta Dey. Pratikshan Mondal. "Nets and sequences of $p$-Bochner, $p$-Dunford and $p$-Pettis integrable functions with values in a Banach space." Funct. Approx. Comment. Math. 63 (1) 43 - 65, September 2020. https://doi.org/10.7169/facm/1818

Information

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

MathSciNet: MR4149510
Digital Object Identifier: 10.7169/facm/1818

Subjects:
Primary: 28A20, 28B05, 40A10, 40A30, 46G10

Rights: Copyright © 2020 Adam Mickiewicz University

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Vol.63 • No. 1 • September 2020
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