Open Access
2016 On VBG Functions and the Denjoy-Khintchine Integral
Brian S. Thomson
Real Anal. Exchange 41(1): 173-226 (2016).


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.


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Brian S. Thomson. "On VBG Functions and the Denjoy-Khintchine Integral." Real Anal. Exchange 41 (1) 173 - 226, 2016.


Published: 2016
First available in Project Euclid: 29 March 2017

zbMATH: 06848922
MathSciNet: MR3511942

Primary: 26A24 , 26A39 , 26A45.

Keywords: ACG function. , approximate derivative , Denjoy-Khintchine integral , variation , VBG function

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 1 • 2016
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