文章基本信息

标题：A note on Riemann integrability
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作者：G. A. Beer
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1978
卷号：1
DOI：10.1155/S0161171278000095
出版社：Hindawi Publishing Corporation
摘要：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.