A Sobolev Space Inroad to Riemann Integrability

Nassar H. S. Haidar^1,

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

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

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.

Keywords:
bounded variation Sobolev space Stieltjes integrals continuity of functions Riemann integrability

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