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A Complete Normed Space of a Class of Guage Integrable Functions

Author

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  • Yassin Alzubaidi
  • Francisco J. Garcia Pacheco

Abstract

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.

Suggested Citation

  • Yassin Alzubaidi & Francisco J. Garcia Pacheco, 2022. "A Complete Normed Space of a Class of Guage Integrable Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-4, November.
    • Handle: RePEc:hin:jjmath:2354758
    DOI: 10.1155/2022/2354758
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