International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 1, Pages 69-73

A note on Riemann integrability

G. A. Beer

Department of Mathematics, California State University, Los Angeles 90032, California, USA

Received 21 November 1977

Copyright © 1978 G. A. Beer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.