A note on Riemann integrability

In this note we define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure. If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set o...

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Main Author:	G. A. Beer
Format:	Article
Language:	English
Published:	Hindawi Limited 1978-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	Riemann integrable functions on a compact metric space compact metric space with Borel measure.
Online Access:	http://dx.doi.org/10.1155/S0161171278000095

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spelling	doaj-f4e357b0afbb483d994f6450049e37632020-11-24T22:04:07ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-0111697310.1155/S0161171278000095A note on Riemann integrabilityG. A. Beer0Department of Mathematics, California State University, Los Angeles 90032, California, USAIn this note we define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure. If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set of points of discontinuity has measure zero.http://dx.doi.org/10.1155/S0161171278000095Riemann integrable functions on a compact metric spacecompact metric space with Borel measure.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	G. A. Beer
spellingShingle	G. A. Beer A note on Riemann integrability International Journal of Mathematics and Mathematical Sciences Riemann integrable functions on a compact metric space compact metric space with Borel measure.
author_facet	G. A. Beer
author_sort	G. A. Beer
title	A note on Riemann integrability
title_short	A note on Riemann integrability
title_full	A note on Riemann integrability
title_fullStr	A note on Riemann integrability
title_full_unstemmed	A note on Riemann integrability
title_sort	note on riemann integrability
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1978-01-01
description	In this note we define Riemann integrabillty for real valued functions defined on a compact metric space accompanied by a finite Borel measure. If the measure of each open ball equals the measure of its corresponding closed ball, then a bounded function is Riemann integrable if and only if its set of points of discontinuity has measure zero.
topic	Riemann integrable functions on a compact metric space compact metric space with Borel measure.
url	http://dx.doi.org/10.1155/S0161171278000095
work_keys_str_mv	AT gabeer anoteonriemannintegrability AT gabeer noteonriemannintegrability
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A note on Riemann integrability

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