Thomson, Brian S. On VBG functions and the Denjoy-Khintchine integral. (English) Zbl 1387.26009 Real Anal. Exch. 41(2015-2016), No. 1, 173-226 (2016). The goal in this work is to obtain a simpler characterization of the Denjoy-Khintchine integral. The authors realize these concepts reworking thoroughly Saks’s treatise using some aspects of the theory of variational measures that capture the concepts of functions of generalized bounded variation (VBG) and functions of generalized absolute continuity (ACG). Then, the reworked theory is used to provide a simpler characterization of the Denjoy-Khintchine integral. Reviewer: Andrey Zahariev (Plovdiv) Cited in 1 Review MSC: 26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems 26A39 Denjoy and Perron integrals, other special integrals 26A45 Functions of bounded variation, generalizations Keywords:variation; approximate derivative; Denjoy-Khintchine integral; generalized absolute continuity; generalized absolute continuity PDFBibTeX XMLCite \textit{B. S. Thomson}, Real Anal. Exch. 41, No. 1, 173--226 (2016; Zbl 1387.26009) Full Text: DOI Euclid