A Complete Normed Space of a Class of Guage Integrable Functions

The space of all gauge integrable functions equipped with the Alexiewicz norm is not a Banach space. This article defines a class of gauge integrable functions that pose a complete normed space under a suitable norm. First, we discuss how the introduced space evolves naturally from the properties of...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
Main Author: Alzubaidi, Yassin
Format: Article
Language:English
Subjects:
Banach spaces
Mathematical functions
Mathematics
Norms
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Summary:The space of all gauge integrable functions equipped with the Alexiewicz norm is not a Banach space. This article defines a class of gauge integrable functions that pose a complete normed space under a suitable norm. First, we discuss how the introduced space evolves naturally from the properties of the gauge integral. Then, we show that this space properly contains the space of all Lebesgue integrable functions. Finally, we prove that it is a Banach space. This result opens the gate for further studies, such as investigating the verity of convergence theorems on the presented space and studying its other properties.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/2354758