Measurable homomorphisms of locally compact groups
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- by Adam Kleppner PDF
- Proc. Amer. Math. Soc. 106 (1989), 391-395 Request permission
Correction: Proc. Amer. Math. Soc. 111 (1991), 1199-1200.
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
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 391-395
- MSC: Primary 22D05; Secondary 28C10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0948154-8
- MathSciNet review: 948154