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September 2010 Universally measurable subgroups of countable index
Christian Rosendal
J. Symbolic Logic 75(3): 1081-1086 (September 2010). DOI: 10.2178/jsl/1278682216

Abstract

It is proved that any countable index, universally measurable subgroup of a Polish group is open. By consequence, any universally measurable homomorphism from a Polish group into the infinite symmetric group S is continuous. It is also shown that a universally measurable homomorphism from a Polish group into a second countable, locally compact group is necessarily continuous.

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Christian Rosendal. "Universally measurable subgroups of countable index." J. Symbolic Logic 75 (3) 1081 - 1086, September 2010. https://doi.org/10.2178/jsl/1278682216

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1200.03035
MathSciNet: MR2723783
Digital Object Identifier: 10.2178/jsl/1278682216

Subjects:
Primary: 03E15 , 43A05

Keywords: ‎automatic continuity , Haar null sets , Universally measurable subgroup

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 3 • September 2010
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