Real functions - current topics
type: Item
instance of: scholarly article
title: Real functions - current topics
zbMATH Open document ID: 0866.26002
author: Vasile Ene
published in: Lecture Notes in Mathematics
publication date: 1995-10-08T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 26-02
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 26A42
zbMATH DE Number: 803192
zbMATH Keywords: Denjoy integral
zbMATH Keywords: Perron integral
zbMATH Keywords: Riemann integral
zbMATH Keywords: Foran integral
zbMATH Keywords: Iseki integral
zbMATH Keywords: nonabsolute integrals
zbMATH Keywords: Kurzweil-Henstock integral
zbMATH Keywords: ACG functions
reviewed by: Peng-Yee Lee
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0095388
OpenAlex ID: W108793125
DOI: 10.1007/BFB0095388
description: scientific article; zbMATH DE number 803192