Universally measurable subgroups of countable index

Christian Rosendal

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arXiv · 1104.3343

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 $S_\infty$ 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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BibTeX RIS

Christian Rosendal. 2011-04-17. Universally measurable subgroups of countable index. https://arxiv.org/abs/1104.3343

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