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A note on a paper of J. D. Stein, Jr.: ``Sequence of regular finitely additive set functions'' (Trans. Amer. Math. Soc. 192 (1974), 59-66)


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 67 (1977), 74-76
MSC: Primary 28A10
MathSciNet review: 0492155
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Abstract: Among other results, it is proved that if a sequence $ \{ {\mu _n}\} $ of regular measures on a Hausdorff space, with values in a normed group, is convergent to zero for all $ \sigma $-compact sets or all open sets, then there exists a maximal open set U such that $ {\dot \mu _n}(U) \to 0,\{ {\dot \mu _n}\} $ being the associated submeasures.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0492155-5
Keywords: Uniformly regular measures, uniformly exhaustive measures, submeasures, equicontinuous submeasures
Article copyright: © Copyright 1977 American Mathematical Society