Journal of Symbolic Logic

Universally measurable subgroups of countable index

Christian Rosendal

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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

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

First available in Project Euclid: 9 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Universally measurable subgroup automatic continuity Haar null sets


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

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