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Proceedings of the American Mathematical Society

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

 

 

The convergence determining class of connected open sets in product spaces


Author: Dieter Landers
Journal: Proc. Amer. Math. Soc. 33 (1972), 529-533
MSC: Primary 60B15; Secondary 28A45
DOI: https://doi.org/10.1090/S0002-9939-1972-0298718-X
MathSciNet review: 0298718
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Abstract: It is proved in this paper that each sequence of measures with values in a topological group--defined on the Borel field of a finite or countable product of connected, locally connected, separable metric spaces--which is Cauchy convergent for all connected open sets is Cauchy convergent for all Borel sets, too.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0298718-X
Keywords: Convergence of measures, connected open sets, product space, topological group
Article copyright: © Copyright 1972 American Mathematical Society