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Transactions of the American Mathematical Society

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

 
 

 

Continuously translating vector-valued measures


Authors: U. B. Tewari and M. Dutta
Journal: Trans. Amer. Math. Soc. 257 (1980), 507-519
MSC: Primary 28B05
DOI: https://doi.org/10.1090/S0002-9947-1980-0552271-0
MathSciNet review: 552271
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Abstract: Let G be a locally compact group and A an arbitrary Banach space. ${L^p}(G,A)$ will denote the space of p-integrable A-valued functions on G. $M(G,A)$ will denote the space of regular A-valued Borel measures of bounded variation on G. In this paper, we characterise the relatively compact subsets of ${L^p}(G,A)$. Using this result, we prove that if $\mu \in M(G,A)$, such that either $x \to {\mu _x}$ or $x{ \to _x}\mu$ is continuous, then $\mu \in {L^1}(G,A)$.


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Keywords: Locally compact group, vector-valued measures
Article copyright: © Copyright 1980 American Mathematical Society