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Convergent sequences of $ \tau $-smooth measures


Author: Surjit Singh Khurana
Journal: Proc. Amer. Math. Soc. 63 (1977), 137-142
MSC: Primary 28A45; Secondary 60B10
DOI: https://doi.org/10.1090/S0002-9939-1977-0435342-4
MathSciNet review: 0435342
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Abstract: It is proved that every $ \tau $-smooth, group-valued Borel measure on a regular Hausdorff space is regular; also it is proved that if a sequence of $ \tau $-smooth Borel measures on a regular Hausdorff space is convergent for regular open sets, then it is convergent for all Borel sets. For a completely regular Hausdorff space, it is proved that if a sequence of Borel $ \tau $-smooth measures is convergent for exactly open sets then it is convergent for all Borel sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0435342-4
Keywords: $ \tau $-smooth measures, regular open sets, submeasures, exhaustive submeasures, finitely additive exhaustive measures
Article copyright: © Copyright 1977 American Mathematical Society

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