FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 3, PAGES 73-83

A new characterization of Riemann-integrable functions

V. K. Zakharov
A. A. Seredinskii

Abstract

View as HTML     View as gif image

In this paper, we describe Riemann-integrable functions with the help of a new class of uniform functions. This description allows us to uncover the “countable” nature of the relation between the space of Riemann-integrable functions and the space of continuous functions. The argumentation is performed for any given topological space $T$ with limited Radon measure $$m the support of which coincides with $T$.

Location: http://mech.math.msu.su/~fpm/eng/k04/k043/k04304h.htm
Last modified: June 2, 2005