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
MathSciNet review: 677236
Abstract: It is well known that a measurable homomorphism from a locally compact group to a topological group must be continuous if is either separable or -compact. In this work it is shown that the above requirement on 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 is a nonopen subgroup of a locally compact group, then under a variety of circumstances, some union of cosets of must fail to be measurable.
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Keywords: Locally compact group, abstract harmonic analysis, Haar measure, nonmeasurable set
Article copyright: © Copyright 1983 American Mathematical Society