Strong Derivative and the Essentially Riemann Integral

We characterize the primitives of Riemann integrable functions using the concept of strong differentiability. We also introduce the notion of essentially Riemann integrable function and characterize it descriptively using its primitive. We also give a characterization of this function that parallels...

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Main Authors:	Calunod, Immanuel D, Garces, Ian June L
Format:	text
Published:	Archīum Ateneo 2021
Subjects:	strong derivative Riemann integral primitive of a Riemann integrable function essentially Riemann integral essentially continuous function essentially bounded function Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/158 https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Strong-derivative-and-the-essentially-Riemann-integral/10.14321/realanalexch.46.1.0233.short
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Institution:	Ateneo De Manila University

id	ph-ateneo-arc.mathematics-faculty-pubs-1167
record_format	eprints
spelling	ph-ateneo-arc.mathematics-faculty-pubs-11672021-11-04T05:22:33Z Strong Derivative and the Essentially Riemann Integral Calunod, Immanuel D Garces, Ian June L We characterize the primitives of Riemann integrable functions using the concept of strong differentiability. We also introduce the notion of essentially Riemann integrable function and characterize it descriptively using its primitive. We also give a characterization of this function that parallels Lebesgue's criterion for Riemann integrability. 2021-10-14T07:00:00Z text https://archium.ateneo.edu/mathematics-faculty-pubs/158 https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Strong-derivative-and-the-essentially-Riemann-integral/10.14321/realanalexch.46.1.0233.short Mathematics Faculty Publications Archīum Ateneo strong derivative Riemann integral primitive of a Riemann integrable function essentially Riemann integral essentially continuous function essentially bounded function Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
continent	Asia
country	Philippines Philippines
content_provider	Ateneo De Manila University Library
collection	archium.Ateneo Institutional Repository
topic	strong derivative Riemann integral primitive of a Riemann integrable function essentially Riemann integral essentially continuous function essentially bounded function Mathematics
spellingShingle	strong derivative Riemann integral primitive of a Riemann integrable function essentially Riemann integral essentially continuous function essentially bounded function Mathematics Calunod, Immanuel D Garces, Ian June L Strong Derivative and the Essentially Riemann Integral
description	We characterize the primitives of Riemann integrable functions using the concept of strong differentiability. We also introduce the notion of essentially Riemann integrable function and characterize it descriptively using its primitive. We also give a characterization of this function that parallels Lebesgue's criterion for Riemann integrability.
format	text
author	Calunod, Immanuel D Garces, Ian June L
author_facet	Calunod, Immanuel D Garces, Ian June L
author_sort	Calunod, Immanuel D
title	Strong Derivative and the Essentially Riemann Integral
title_short	Strong Derivative and the Essentially Riemann Integral
title_full	Strong Derivative and the Essentially Riemann Integral
title_fullStr	Strong Derivative and the Essentially Riemann Integral
title_full_unstemmed	Strong Derivative and the Essentially Riemann Integral
title_sort	strong derivative and the essentially riemann integral
publisher	Archīum Ateneo
publishDate	2021
url	https://archium.ateneo.edu/mathematics-faculty-pubs/158 https://projecteuclid.org/journals/real-analysis-exchange/volume-46/issue-1/Strong-derivative-and-the-essentially-Riemann-integral/10.14321/realanalexch.46.1.0233.short
_version_	1718383530088595456

Strong Derivative and the Essentially Riemann Integral

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