{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T11:15:41Z","timestamp":1648811741227},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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 <jats:italic>S<\/jats:italic><jats:sub>\u221e<\/jats:sub> 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.<\/jats:p>","DOI":"10.2178\/jsl\/1278682216","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T09:30:45Z","timestamp":1278667845000},"page":"1081-1086","source":"Crossref","is-referenced-by-count":3,"title":["Universally measurable subgroups of countable index"],"prefix":"10.1017","volume":"75","author":[{"given":"Christian","family":"Rosendal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002541_ref001","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-11010"},{"key":"S0022481200002541_ref005","doi-asserted-by":"publisher","DOI":"10.2178\/bsl\/1243948486"},{"key":"S0022481200002541_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/S002461150601584X"},{"key":"S0022481200002541_ref002","volume-title":"Topology and Borel structure. Descriptive topology and set theory with applications to functional analysis and measure theory","volume":"10","author":"Christensen","year":"1974"},{"key":"S0022481200002541_ref003","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdl007"},{"key":"S0022481200002541_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/fm-61-2-165-169"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002541","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T17:38:39Z","timestamp":1556386719000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002541\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0022481200002541"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1278682216","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}