Two results for monocompact measures
type: Item
instance of: scholarly article
title: Two results for monocompact measures
zbMATH Open document ID: 0803.28003
DOI: 10.1007/BF03026557
author: Monika Dekiert
published in: Manuscripta Mathematica
publication date: 1995-01-02T00:00:00Z
full work available at URL: https://eudml.org/doc/155879
review text: The author proves that a finite measure defined on an \(\omega_ 1\)- generated \(\sigma\)-algebra of sets is monocompact if and only if it is compact [this gives a partial answer to a question of \textit{F. Topsøe} posed in Colloq. Math. 42, 377-385 (1979; Zbl 0448.28001), whether monocompact measures are compact]. As a consequence, the author gets the result that an example constructed by the reviewer in Lect. Notes Math. 541, 31-42 (1976; Zbl 0341.28003) of a perfect but non-compact measure is in fact an example of a perfect and not monocompact measure (this answers another question of Topsøe [also \textit{D. Ramachandran}, ``Perfect measures. II'' (1979; Zbl 0523.60006)], whether the notions of perfectness and monocompactness are equivalent). That monocompactness implies perfectness was proved earlier by Pachl (\textit{F. Topsøe}, ibid.).
Mathematics Subject Classification ID: 28A12
zbMATH DE Number: 492790
zbMATH Keywords: compact measures
zbMATH Keywords: perfect measures
zbMATH Keywords: monocompact measures
reviewed by: Kazimierz Musial
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 492790