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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Automatic continuity of measurable group homomorphisms


Author: Jonathan W. Lewin
Journal: Proc. Amer. Math. Soc. 87 (1983), 78-82
MSC: Primary 22D05; Secondary 22A05, 43A22
DOI: https://doi.org/10.1090/S0002-9939-1983-0677236-8
MathSciNet review: 677236
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Abstract: It is well known that a measurable homomorphism from a locally compact group $ G$ to a topological group $ Y$ must be continuous if $ Y$ is either separable or $ \sigma $-compact. In this work it is shown that the above requirement on $ Y$ can be somewhat relaxed and it is shown inter alia that a measurable homomorphism from a locally compact group to a locally compact abelian group will always be continuous. In addition, it is shown that if $ H$ is a nonopen subgroup of a locally compact group, then under a variety of circumstances, some union of cosets of $ H$ must fail to be measurable.


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

  • [1] Michael G. Cowling, Spaces $ A_p^q$ and $ {L^p} - {L^q}$ Fourier multipliers, Ph.D. Thesis, Flinders University of South Australia, December 1973.
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0677236-8
Keywords: Locally compact group, abstract harmonic analysis, Haar measure, nonmeasurable set
Article copyright: © Copyright 1983 American Mathematical Society