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Universally measurable subgroups of countable index
Published online by Cambridge University Press: 12 March 2014
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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- Copyright © Association for Symbolic Logic 2010
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