Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 75, Issue 3 (2010), 1081-1086.
Universally measurable subgroups of countable index
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.
J. Symbolic Logic, Volume 75, Issue 3 (2010), 1081-1086.
First available in Project Euclid: 9 July 2010
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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