Universally measurable subgroups of countable index

Journal of Symbolic Logic 75 (3):1081-1086 (2010)
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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

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10.2178/jsl/1278682216

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Automatic continuity of group homomorphisms.Christian Rosendal - 2009 - Bulletin of Symbolic Logic 15 (2):184-214.

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