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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Measurable homomorphisms of locally compact groups


Author: Adam Kleppner
Journal: Proc. Amer. Math. Soc. 106 (1989), 391-395
MSC: Primary 22D05; Secondary 28C10
MathSciNet review: 948154
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Abstract: Let $ G$ and $ H$ be locally compact groups and $ \varphi $ a homomorphism from $ G$ into $ H$. Suppose that $ {\varphi ^{ - 1}}\left( U \right)$ is measurable for every open set $ U \subset H$. It is known under some conditions, for example, if $ H$ is $ \sigma $-compact, that $ \varphi $ is continuous. Here it is shown that this result is true without any countability restrictions on $ G$ and $ H$. The proof depends on the observation that the regular representation of $ H$ is a homomorphism.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0948154-8
PII: S 0002-9939(1989)0948154-8
Article copyright: © Copyright 1989 American Mathematical Society