Continuity of \(\delta\)-variation and construction of continuous major and minor functions for the Perron integral (Q1912731)

It is a well-known result of Saks that the Perron integral defined by arbitrary major/minor functions, can just as well be obtained using continuous major/minor functions. However, the construction of such functions is far from obvious. In this interesting paper, the author gives such a construction by first showing that the left/right \(\delta\)-variations of a continuous function are also continuous. The use of left/right \(\delta\)-variations rather than just the \(\delta\)-variation is essential; a point missed in some earlier papers on this subject.