On the descriptive definition of the Burkill approximately continuous integral
type: Item
instance of: scholarly article
title: On the descriptive definition of the Burkill approximately continuous integral
zbMATH Open document ID: 0774.26006
published in: Real Analysis Exchange
publication date: 1993-06-29T00:00:00Z
review text: In a paper of the reviewer [J. Aust. Math. Soc., Ser. A 35, 236-253 (1983; Zbl 0533.26005)] a class of functions, called \([\text{ACG}_{ap}^*]\) functions was defined; this class was then shown to be identical to the class of primitives of the approximately continuous Perron integral of Burkill, the AP-integral. In this paper an example is given that shows the characterization is incorrect. A function is constructed that is AP-integrable, but the primitive of this function is not \([\text{ACG}_{ap}^*]\). The author points out where the error occurs and says he is working on a correct definition for the class of \([\text{ACG}_{ap}^*]\) functions.
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 222106
zbMATH Keywords: approximately continuous Perron integral of Burkill
zbMATH Keywords: AP-integral
author: Ke-Cheng Liao
reviewed by: P. S. Bullen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 222106