International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 1, Pages 69-74
doi:10.1155/S0161171278000095
A note on Riemann integrability
G.A. Beer
Department of Mathematics, California State University, Los Angeles 90032, California, USA
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.