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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A generalized topological measure theory


Authors: R. B. Kirk and J. A. Crenshaw
Journal: Trans. Amer. Math. Soc. 207 (1975), 189-217
MSC: Primary 28A32
DOI: https://doi.org/10.1090/S0002-9947-1975-0369648-7
MathSciNet review: 0369648
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Abstract: The theory of measures in a topological space, as developed by V. S. Varadarajan for the algebra $ {C^b}$ of bounded continuous functions on a completely regular topological space, is extended to the context of an arbitrary uniformly closed algebra $ A$ of bounded real-valued functions. Necessary and sufficient conditions are given for $ {A^ \ast }$ to be represented in the natural way by a space of regular finitely-additive set functions. The concepts of additivity and tightness for these set functions are considered and some remarks about weak convergence are made.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0369648-7
Keywords: Measures in topological spaces, Frink's conjecture, additivity, tightness, representation, finitely-additive set function, normal base
Article copyright: © Copyright 1975 American Mathematical Society