{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T16:36:08Z","timestamp":1772037368533,"version":"3.50.1"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"the NSF CAREER","award":["DMS-1651321"],"award-info":[{"award-number":["DMS-1651321"]}]},{"name":"the Narodowe Centrum Nauki","award":["2016\/22\/E\/ST1\/00450"],"award-info":[{"award-number":["2016\/22\/E\/ST1\/00450"]}]},{"name":"the Narodowe Centrum Nauki","award":["2018\/31\/B\/ST\/00357"],"award-info":[{"award-number":["2018\/31\/B\/ST\/00357"]}]},{"name":"the Science Fund of the Republic of Serbia","award":["7750027\u2013SMART"],"award-info":[{"award-number":["7750027\u2013SMART"]}]},{"name":"NSF","award":["DMS-1665035"],"award-info":[{"award-number":["DMS-1665035"]}]},{"name":"NSF","award":["DMS-1760212"],"award-info":[{"award-number":["DMS-1760212"]}]},{"name":"NSF","award":["DMS-2054271"],"award-info":[{"award-number":["DMS-2054271"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p>We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups.<\/jats:p>","DOI":"10.1142\/s0219061322500258","type":"journal-article","created":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T03:29:30Z","timestamp":1659929370000},"source":"Crossref","is-referenced-by-count":3,"title":["Invariant measures in simple and in small theories"],"prefix":"10.1142","volume":"23","author":[{"given":"Artem","family":"Chernikov","sequence":"first","affiliation":[{"name":"UCLA, Los Angeles, CA 90095, USA"}]},{"given":"Ehud","family":"Hrushovski","sequence":"additional","affiliation":[{"name":"University of Oxford, Oxford, UK"}]},{"given":"Alex","family":"Kruckman","sequence":"additional","affiliation":[{"name":"Wesleyan University, Middletown, CT 06459, USA"}]},{"given":"Krzysztof","family":"Krupi\u0144ski","sequence":"additional","affiliation":[{"name":"Instytut Matematyczny, Uniwersytet Wroc\u0142awski, Pl. 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