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.
"Universally measurable subgroups of countable index." J. Symbolic Logic 75 (3) 1081 - 1086, September 2010. https://doi.org/10.2178/jsl/1278682216