Journal of Symbolic Logic

Universally measurable subgroups of countable index

Christian Rosendal

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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.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 3 (2010), 1081-1086.

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682216

Digital Object Identifier
doi:10.2178/jsl/1278682216

Mathematical Reviews number (MathSciNet)
MR2723783

Zentralblatt MATH identifier
1200.03035

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 43A05: Measures on groups and semigroups, etc.

Keywords
Universally measurable subgroup automatic continuity Haar null sets

Citation

Rosendal, Christian. Universally measurable subgroups of countable index. J. Symbolic Logic 75 (2010), no. 3, 1081--1086. doi:10.2178/jsl/1278682216. https://projecteuclid.org/euclid.jsl/1278682216


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