On VBG Functions and the Denjoy-Khintchine Integral

Brian S. Thomson

doi:rae/1490752823

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Home > Journals > Real Anal. Exchange > Volume 41 > Issue 1 > Article

2016 On VBG Functions and the Denjoy-Khintchine Integral

Brian S. Thomson

Real Anal. Exchange 41(1): 173-226 (2016).

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Abstract

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.