Geodesic
A~new characterization of Riemann-integrable functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 73-83.

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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 $\mu$ the support of which coincides with $T$. 
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V. K. Zakharov; A. A. Seredinskii. A~new characterization of Riemann-integrable functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 73-83. http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a3/

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