Automatic continuity of measurable group homomorphisms
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- by Jonathan W. Lewin PDF
- Proc. Amer. Math. Soc. 87 (1983), 78-82 Request permission
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
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Michael G. Cowling, Spaces $A_p^q$ and ${L^p} - {L^q}$ Fourier multipliers, Ph.D. Thesis, Flinders University of South Australia, December 1973.
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der mathematischen Wissenschaften, Band 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156915
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
Additional Information
- © Copyright 1983 American Mathematical Society
- 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