{"title":"Kudō-continuity条件熵","authors":"M. Björklund, Yair Hartman, Hanna Oppelmayer","doi":"10.1214/22-aihp1313","DOIUrl":null,"url":null,"abstract":". In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kudō-continuity of conditional entropies\",\"authors\":\"M. Björklund, Yair Hartman, Hanna Oppelmayer\",\"doi\":\"10.1214/22-aihp1313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.\",\"PeriodicalId\":42884,\"journal\":{\"name\":\"Annales de l Institut Henri Poincare D\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de l Institut Henri Poincare D\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/22-aihp1313\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-aihp1313","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
. In this paper we introduce the notion of Kudo-continuity for real-valued functions on the space of all complete sub- σ -algebras of a standard probability space. This is an a priori strengthening of continuity with respect to strong convergence. We show that conditional entropies are Kudo-continuous, and discuss an application to the study of Furstenberg entropy spectra of SAT*-spaces.
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