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Diestel, J. and Uhl, J. J, Vector measures, AMS, Providence, RI, 1977.

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Article

A Sobolev Space Inroad to Riemann Integrability

1CRAMS: Center for Research in Applied Mathematics & Statistics, AUL, Beirut, Lebanon


Turkish Journal of Analysis and Number Theory. 2020, Vol. 8 No. 2, 34-38
DOI: 10.12691/tjant-8-2-3
Copyright © 2020 Science and Education Publishing

Cite this paper:
Nassar H. S. Haidar. A Sobolev Space Inroad to Riemann Integrability. Turkish Journal of Analysis and Number Theory. 2020; 8(2):34-38. doi: 10.12691/tjant-8-2-3.

Correspondence to: Nassar  H. S. Haidar, CRAMS: Center for Research in Applied Mathematics & Statistics, AUL, Beirut, Lebanon. Email: nhaidar@suffolk.edu

Abstract

A conditioned equivalence is proved for a certain weighted Sobolev space to the space of Riemann integrable functions. An equivalence representing a new result that not only asserts the sufficiency (but non-necessity) nature of bounded variation of functions for their Riemann integrability, but also reveals a potential for some novel computational findings.

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