Real Analysis Exchange

On VBG Functions and the Denjoy-Khintchine Integral

Brian S. Thomson

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The study of functions of generalized bounded variation (VBG) and generalized absolute continuity (ACG) that appears in Saks’s treatise Theory of the Integral can be thoroughly reworked by using some aspects of the theory of variational measures proposed originally by Ralph Henstock and extended by many others. We present a development of these concepts and use it for a characterization of the Denjoy-Khintchine integral.

Article information

Real Anal. Exchange, Volume 41, Number 1 (2016), 173-226.

First available in Project Euclid: 29 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

variation approximate derivative Denjoy-Khintchine integral VBG function ACG function.


Thomson, Brian S. On VBG Functions and the Denjoy-Khintchine Integral. Real Anal. Exchange 41 (2016), no. 1, 173--226.

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