Quasi-Radon measures and Radon measures of type (\(\mathcal H\))
type: Item
instance of: scholarly article
title: Quasi-Radon measures and Radon measures of type (\(\mathcal H\))
zbMATH Open document ID: 0728.28012
DOI: 10.1007/BF02846367
author: Baltasar Rodríguez-Salinas
publication date: 1991-01-01T00:00:00Z
review text: It is well-known that every Radon measure on a topological space (introduced by L. Schwartz in 1973) is a locally finite Radon measure of type (\({\mathcal K})\), \({\mathcal K}\) being the family of all compact subsets of the space. The object of this paper is to state the relations between the quasi-Radon measures (defined by D. H. Fremlin in 1974) and the Radon measures of type (\({\mathcal H})\) (defined by the author in 1973), proving that every quasi-Radon measure is a complete and locally determined Radon measure of type (\({\mathcal F}_ 0)\), where \({\mathcal F}_ 0\) denotes the class of the closed subsets of finite measure, and that every almost everywhere locally finite, complete and locally determined Radon measure of type (\({\mathcal H})\) is a quasi-Radon measure. So there exist Radon measures of type (\({\mathcal H})\) which are not quasi-Radon. It is also possible to find Radon measures of type (\({\mathcal H})\) which are not Radon.
Mathematics Subject Classification ID: 28C15
zbMATH DE Number: 4202640
zbMATH Keywords: Radon measure
zbMATH Keywords: quasi-Radon measure
zbMATH Keywords: complete
reviewed by: P. Jiménez Guerra
MaRDI profile type: Publication
cites work: Pre-Radon measures on topological spaces
cites work: Q4750916
cites work: Q5182141
cites work: Products of Radon Measures: A Counter-Example
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4202640