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Universally measurable subgroups of countable index

Published online by Cambridge University Press:  12 March 2014

Christian Rosendal
Christian Rosendal*
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St. Chicago, Il 60607-7045, USA. E-mail: rosendal@math.uic.edu, URL: http://www.math.uic.edu/~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∞ 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.

Keywords

Universally measurable subgroupautomatic continuityHaar null sets
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 3 , September 2010 , pp. 1081 - 1086
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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