On the Alexiewicz topology of the Denjoy space
type: Item
instance of: scholarly article
title: On the Alexiewicz topology of the Denjoy space
zbMATH Open document ID: 0879.26028
author: Thiruvaiyaru V. Panchapagesan
author: Benedetto Bongiorno
published in: Real Analysis Exchange
publication date: 1997-12-10T00:00:00Z
review text: The space \(H\) of all Denjoy-Perron integrable functions on \([a,b]\) endowed with the Alexiewicz norm \(|f|_H=\sup_{x}|\int_a^xf(t) dt|\) is the Denjoy space of \([a,b]\). The completion \(\mathcal H\) of \(H\) is also studied and some previous results of the first author concerning the characterization of relatively (weakly) compact subsets of \(H\) and \(\mathcal H\) are completed and enhanced in the paper.
Mathematics Subject Classification ID: 26A39
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 1095852
zbMATH Keywords: Denjoy space
zbMATH Keywords: Alexiewicz norm
zbMATH Keywords: completion
zbMATH Keywords: relatively weakly compact set
zbMATH Keywords: Denjoy-Perron integrable functions
reviewed by: Štefan Schwabik
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1095852