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A new characterization of Riemann-integrable functions

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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 μ the support of which coincides with T.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 3, pp. 73–83, 2004.

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Zakharov, V.K., Seredinskii, A.A. A new characterization of Riemann-integrable functions. J Math Sci 139, 6708–6714 (2006).

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  • Bounded Function
  • Full Measure
  • Discontinuity Point
  • Semicontinuous Function
  • Regularization Function