{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T08:19:34Z","timestamp":1648714774338},"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":15533,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1971,9]]},"abstract":"<jats:p>In this paper we prove some theorems concerning measures on complete Boolean algebras. Among other things, in \u00a7I of this paper, we construct a counterexample to the following conjecture of W. Luxemburg: Every measure on a nonatomic hyperstonian Boolean algebra is normal. (See [3, p. 57].) This result is expressed by Theorem 1, \u00a7I. In order to construct this example we have to suppose that a real-valued measurable cardinal exists. This hypothesis is independent of the usual axioms of set theory. Luxemburg proved that our assumption is necessary. Our second result is stated in Theorem 2 near the end of the paper.<\/jats:p>","DOI":"10.2307\/2269947","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:09:50Z","timestamp":1146949790000},"page":"395-406","source":"Crossref","is-referenced-by-count":1,"title":["On measures on complete Boolean algebras"],"prefix":"10.1017","volume":"36","author":[{"given":"Karel","family":"Prikry","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200082190_ref005","first-page":"5","article-title":"Changing measurable into accessible cardinals","volume":"68","author":"Prikry","year":"1970","journal-title":"Dissertationes Mathematicae"},{"key":"S0022481200082190_ref004","doi-asserted-by":"publisher","DOI":"10.4064\/cm-22-2-209-214"},{"key":"S0022481200082190_ref006","volume-title":"Boolean algebras","author":"Sikorski","year":"1964"},{"key":"S0022481200082190_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9440-2"},{"key":"S0022481200082190_ref002","doi-asserted-by":"publisher","DOI":"10.4064\/fm-53-3-225-308"},{"key":"S0022481200082190_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/cm-19-1-51-58"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200082190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T19:53:29Z","timestamp":1559332409000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200082190\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1971,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1971,9]]}},"alternative-id":["S0022481200082190"],"URL":"https:\/\/doi.org\/10.2307\/2269947","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1971,9]]}}}