Real functions - current topics
The author gives a list of the nonabsolute integrals including those in \textit{S. Saks} [Theory of the integral (1937; Zbl 0017.30004)] and many others which were developed afterwards. They are of the Perron type using major and minor functions, of the Denjoy type using derivatives or approximate derivatives, and of the Riemann type (in particular the Kurzweil-Henstock integral [see, for example, \textit{P.-Y. Lee}: ``Lanzhou lectures on Henstock integration'' (1989; Zbl 0699.26004)]). The final result is a descriptive definition of an integral (i.e., of the Denjoy type) which includes both Foran's integral and Iseki's sparse integral. The book contains also an exhaustive list of various kinds of ACG functions (generalized absolutely continuous functions), a general monotonicity theorem, and 66 examples and counterexamples.
scientific article; zbMATH DE number 803192