Translator Disclaimer
2020 A Generalization of the Riemann-Lebesgue Theorem for Riemann Integrability
Otgonbayar Uuye
Real Anal. Exchange 45(2): 481-486 (2020). DOI: 10.14321/realanalexch.45.2.0481

Abstract

A classical theorem of Riemann and Lebesgue says that a bounded function defined on a compact interval is Riemann integrable if and only if it is continuous almost everywhere. In this note, we generalize their result and show that the difference between the upper and lower Riemann integrals of a not necessarily Riemann integrable function equals the upper Riemann integral of its oscillation function.

Citation

Download Citation

Otgonbayar Uuye. "A Generalization of the Riemann-Lebesgue Theorem for Riemann Integrability." Real Anal. Exchange 45 (2) 481 - 486, 2020. https://doi.org/10.14321/realanalexch.45.2.0481

Information

Published: 2020
First available in Project Euclid: 30 June 2020

zbMATH: 07229060
Digital Object Identifier: 10.14321/realanalexch.45.2.0481

Subjects:
Primary: 26A42
Secondary: 26A06

Rights: Copyright © 2020 Michigan State University Press

JOURNAL ARTICLE
6 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.45 • No. 2 • 2020
Back to Top