On p-adic vector measure spaces
type: Item
instance of: scholarly article
title: On p-adic vector measure spaces
zbMATH Open document ID: 1191.46061
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-02-19T00:00:00Z
review text: The author has made important contributions to non-archimedean measure theory. The present paper is one of them. It is the natural continuation of his previous works about spaces of measures with values in a complete non-archimedean locally convex space \(E\). After a first preliminary section, the author studies in Section~2 the measurable sets and the integrable functions over them, with respect to a measure \(m\) defined in a separating algebra of subsets of a non-empty set and with values in \(E\). Measurable functions are introduced and treated in Section~3, where the author obtains some characterizations as well as some stability properties for this kind of functions. Finally, in Section~4, the concept of convergence in measure is given and investigated, and also several relations of this concept with the \(m\)-integrable functions are established. The study of the subject of every section is carried out in a deep and elegant way. I recommend this paper to any person interested in non-archimedean vector measure theory.
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 28B05
zbMATH DE Number: 5673285
zbMATH Keywords: non-archimedean fields
zbMATH Keywords: \(p\)-adic measures
zbMATH Keywords: locally convex spaces
zbMATH Keywords: measurable functiosn
zbMATH Keywords: convergence in measure
author: A. K. Katsaras
reviewed by: Cristina Pérez-García
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.10.059
OpenAlex ID: W1985304087
cites work: Q3369301
cites work: Non-archimedean vector measures and integral operators
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DOI: 10.1016/J.JMAA.2009.10.059
description: scientific article; zbMATH DE number 5673285