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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The convergence determining class of regular open sets


Author: Lothar Rogge
Journal: Proc. Amer. Math. Soc. 37 (1973), 581-585
MSC: Primary 28A45; Secondary 60B05
MathSciNet review: 0311872
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Abstract: The purpose of this paper is to prove that every sequence of closed approximate measures defined on the Borel-field of a normal topological space with values in an abelian topological group is Cauchy convergent for all Borel sets if it is Cauchy convergent for all regular open sets. In particular every sequence of measures on the Borel-field of a perfectly normal topological space which is Cauchy convergent for all regular open sets is Cauchy convergent for all Borel sets, too.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0311872-7
Keywords: Convergence of measures, regular open sets, topological group
Article copyright: © Copyright 1973 American Mathematical Society