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Transactions of the American Mathematical Society
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
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0552271-0
PII: S 0002-9947(1980)0552271-0
Keywords: Locally compact group, vector-valued measures
Article copyright: © Copyright 1980 American Mathematical Society