On convergence theorems for the AP integral
type: Item
instance of: scholarly article
title: On convergence theorems for the AP integral
zbMATH Open document ID: 0804.26007
published in: Southeast Asian Bulletin of Mathematics
publication date: 1995-01-12T00:00:00Z
review text: This paper extends to the approximate Perron integral of Burkill [\textit{J. C. Burkill}, Math. Z. 34, 270-278 (1931; Zbl 0002.38604); the reviewer, J. Aust. Mat. Soc., Ser. A 35, 236-253 (1983; Zbl 0533.26005)] the recent limit theorems, known as controlled convergence theorems, that were proved for the Henstock-Kurzweil (= Denjoy-Perron) integral [see \textit{P.- Y. Lee}: ``Lanzhou lectures on Henstock integration'' (1989; Zbl 0699.26004)]. These controlled convergence theorems occur in several forms depending on the kind of uniformity condition applied to the converging sequence of functions. Some of these conditions are extended to the approximate case and the appropriate convergence theorems are then proved.
Mathematics Subject Classification ID: 26A39
zbMATH DE Number: 563430
zbMATH Keywords: AP integral
zbMATH Keywords: approximate Perron integral of Burkill
zbMATH Keywords: limit theorems
zbMATH Keywords: controlled convergence theorems
author: Shi Pan Lu
reviewed by: P. S. Bullen
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 563430