Topological vector spaces of Bochner measurable functions
type: Item
instance of: scholarly article
title: Topological vector spaces of Bochner measurable functions
zbMATH Open document ID: 1024.46011
author: Iwo Labuda
author: Lech Drewnowski
published in: Illinois Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: The authors introduce the notion of a topological vector space of Bochner measurable functions defined on a submeasure space and taking their values in a complete metrizable topological vector space. This general notion provides a framework where, as shown in the paper, many familiar results from the theory of Banach lattices, topological Riesz spaces and Lebesgue-Bochner spaces remain true. Among the many interesting results given in this paper, we will mention just a few; namely, the characterizations of Lebesgue and Levi type properties; the characterizations of topological, sequential, and monotone completeness; Orlicz-Pettis type theorems; and the inclusion of copies of \(c_0\) and \(\ell^\infty\).
reviewed by: Pedro J. Paúl
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 1839947
zbMATH Keywords: Banach lattices
zbMATH Keywords: Lebesgue property
zbMATH Keywords: Bochner integral
zbMATH Keywords: Levi type properties
zbMATH Keywords: completeness
zbMATH Keywords: Orlicz-Pettis type theorems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839947