A note on Riemann integrability

G. A. Beer

International Journal of Mathematics and Mathematical Sciences, 1978, vol. 1, 1-5

Abstract:

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.

Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:729802

DOI: 10.1155/S0161171278000095

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