Continuously translating vector-valued measures
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- by U. B. Tewari and M. Dutta PDF
- Trans. Amer. Math. Soc. 257 (1980), 507-519 Request permission
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 $\mu \in {L^1}(G,A)$.References
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Additional Information
- © Copyright 1980 American Mathematical Society
- 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