Real Analysis Exchange

The Space of Denjoy-Perron Integrable Functions

Brian S. Thomson

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In the linear space$\mathcal{DP}[a,b]$ of all Denjoy-Perron integrable functions on an interval $[a,b]$ one wishes to introduce the most natural topology. Herein are some considerations that suggest what topology might be the most natural.

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Real Anal. Exchange, Volume 25, Number 2 (1999), 711-726.

First available in Project Euclid: 3 January 2009

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Zentralblatt MATH identifier

Primary: 26A45: Functions of bounded variation, generalizations 26A39: Denjoy and Perron integrals, other special integrals 26A46: Absolutely continuous functions 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]

Denjoy-Perron integral Alexiewicz norm


Thomson, Brian S. The Space of Denjoy-Perron Integrable Functions. Real Anal. Exchange 25 (1999), no. 2, 711--726.

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