Some equivalents of the \(AP\) controlled convergence theorem, their generalizations and a Riesz-type definition of the \(AP\)-integral
type: Item
instance of: scholarly article
title: Some equivalents of the \(AP\) controlled convergence theorem, their generalizations and a Riesz-type definition of the \(AP\)-integral
zbMATH Open document ID: 0831.26001
published in: Real Analysis Exchange
publication date: 1995-11-09T00:00:00Z
review text: The approximately continuous Perron integral was defined by \textit{J. C. Burkill} [Math. Z. 34, 270-278 (1931; Zbl 0002.38604)]. A convergence theorem known as the controlled convergence theorem for the integral has been proved [see the author, Real Anal. Exch. 19, No. 1, 212-217 (1994; Zbl 0804.26006)]. The author gives various equivalents of the controlled convergence, and, as a consequence, provides a Riesz-type definition of the integral.
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 801027
zbMATH Keywords: approximately continuous Perron integral
zbMATH Keywords: controlled convergence theorem
zbMATH Keywords: Riesz-type definition of the integral
author: Ke-Cheng Liao
reviewed by: Peng-Yee Lee
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 801027