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On VBG functions and the Denjoy-Khintchine integral. (English) Zbl 1387.26009

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.

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
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