{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:23:08Z","timestamp":1760170988943},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2016,12,27]],"date-time":"2016-12-27T00:00:00Z","timestamp":1482796800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2017,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>\u03ba<\/jats:italic> be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that <jats:italic>\u03ba<\/jats:italic> is not a weakly inaccessible cardinal, we show that each probability that is not <jats:italic>\u03ba<\/jats:italic>-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than <jats:italic>\u03ba<\/jats:italic>. This generalizes a result of Schervish, Seidenfeld, &amp; Kadane (1984), which established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition.<\/jats:p>","DOI":"10.1017\/s1755020316000344","type":"journal-article","created":{"date-parts":[[2016,12,27]],"date-time":"2016-12-27T12:53:11Z","timestamp":1482843191000},"page":"284-300","source":"Crossref","is-referenced-by-count":10,"title":["NONCONGLOMERABILITY FOR COUNTABLY ADDITIVE MEASURES THAT ARE NOT <i>\u03ba<\/i>-ADDITIVE"],"prefix":"10.1017","volume":"10","author":[{"given":"MARK J.","family":"SCHERVISH","sequence":"first","affiliation":[]},{"given":"TEDDY","family":"SEIDENFELD","sequence":"additional","affiliation":[]},{"given":"JOSEPH B.","family":"KADANE","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,12,27]]},"reference":[{"key":"S1755020316000344_ref1","first-page":"105","article-title":"\u03ba-finiteness and \u03ba-additivity of measures on sets and left invariant measures on discrete groups","volume":"80","author":"Armstrong","year":"1980","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S1755020316000344_ref9","first-page":"59","volume-title":"Bayesian Inference and Decision Techniques","author":"Kadane","year":"1986"},{"key":"S1755020316000344_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996451"},{"key":"S1755020316000344_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00531529"},{"key":"S1755020316000344_ref8","volume-title":"Set Theory","author":"Jech","year":"1978"},{"key":"S1755020316000344_ref2","volume-title":"Probability and Measure","author":"Billingsley","year":"1995"},{"key":"S1755020316000344_ref13","doi-asserted-by":"crossref","first-page":"1612","DOI":"10.1214\/aop\/1015345764","article-title":"Improper regular conditional distributions","volume":"29","author":"Seidenfeld","year":"2001","journal-title":"Annals of Probability"},{"key":"S1755020316000344_ref6","first-page":"139","article-title":"Eine Bemerkung zur Theorie der regressiven Funktionen","volume":"17","author":"Fodor","year":"1956","journal-title":"Acta Scientiarum Mathematicarum (Szeged)"},{"key":"S1755020316000344_ref14","doi-asserted-by":"crossref","first-page":"140","DOI":"10.4064\/fm-16-1-140-150","article-title":"Zur Masstheorie in der allgemeinen Mengenlehre","volume":"16","author":"Ulam","year":"1930","journal-title":"Fundamenta Mathematicae"},{"key":"S1755020316000344_ref11","volume-title":"Foundations of the Theory of Probability","author":"Kolmogorov","year":"1956"},{"key":"S1755020316000344_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0877-8"},{"key":"S1755020316000344_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9440-2"},{"key":"S1755020316000344_ref3","volume-title":"Theory of Probability","author":"de Fineitti","year":"1974"},{"key":"S1755020316000344_ref10","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476992"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020316000344","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T21:46:37Z","timestamp":1555537597000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020316000344\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,27]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["S1755020316000344"],"URL":"https:\/\/doi.org\/10.1017\/s1755020316000344","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,27]]}}}