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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Uniformly distributed sequences in locally compact groups. II


Author: Leonora Benzinger
Journal: Trans. Amer. Math. Soc. 188 (1974), 167-178
MSC: Primary 22D05; Secondary 10K99
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Abstract: We consider the following question. When is there a compactification $ {G_0}$ of a locally compact group G (recall that a compact group $ {G_0}$ is a compactification of G if there is a continuous homomorphism $ \phi :G \to {G_0}$ so that $ \phi (G)$ is dense in G) with continuous homomorphism $ \phi :G \to {G_0}$ with the property that $ \{ {g_\nu }\} $ is uniformly distributed in G if and only if $ \{ \phi ({g_\nu })\} $ is uniformly distributed in $ {G_0}$? Such a compactification $ {G_0}$ is called a D-compactification of G. We obtain a solution to this problem and thereby generalize to locally compact groups some results of Berg, Rajagopalan, and Rubel concerning D-compactifications of locally compact abelian groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-74-99944-9
PII: S 0002-9947(74)99944-9
Keywords: Locally compact group, uniform distribution, compactification, D-compactification
Article copyright: © Copyright 1974 American Mathematical Society