{"title":"On the Boolean algebra tensor product via Carathéodory spaces of place functions","authors":"G. Buskes, Page Thorn","doi":"10.1090/bproc/161","DOIUrl":null,"url":null,"abstract":"We show that the Carathéodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with Fremlin’s Archimedean Riesz space tensor product of their respective Carathéodory spaces of place functions. We provide a solution to Fremlin’s problem 315Y(f) [Measure Theory, Torres Fremlin, Colchester, 2004] concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carathéodory spaces of place functions.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/161","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We show that the Carathéodory space of place functions on the free product of two Boolean algebras is Riesz isomorphic with Fremlin’s Archimedean Riesz space tensor product of their respective Carathéodory spaces of place functions. We provide a solution to Fremlin’s problem 315Y(f) [Measure Theory, Torres Fremlin, Colchester, 2004] concerning completeness in the free product of Boolean algebras by applying our results on the Archimedean Riesz space tensor product to Carathéodory spaces of place functions.
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