{"title":"Some duality results for equivalence couplings and total variation","authors":"L. Pratelli, P. Rigo","doi":"10.1214/24-ecp586","DOIUrl":null,"url":null,"abstract":". Let (Ω , F ) be a standard Borel space and P ( F ) the collection of all probability measures on F . Let E ⊂ Ω × Ω be a measurable equivalence relation, that is, E ∈ F⊗F and the relation on Ω defined as x ∼ y ⇔ ( x,y ) ∈ E is reflexive, symmetric and transitive. It is shown that there are two σ -fields G 0 and G 1 on Ω such that, for all µ, ν ∈ P ( F ),","PeriodicalId":0,"journal":{"name":"","volume":"40 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/24-ecp586","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
. Let (Ω , F ) be a standard Borel space and P ( F ) the collection of all probability measures on F . Let E ⊂ Ω × Ω be a measurable equivalence relation, that is, E ∈ F⊗F and the relation on Ω defined as x ∼ y ⇔ ( x,y ) ∈ E is reflexive, symmetric and transitive. It is shown that there are two σ -fields G 0 and G 1 on Ω such that, for all µ, ν ∈ P ( F ),
.让 (Ω , F ) 是一个标准的 Borel 空间，P ( F ) 是 F 上所有概率度量的集合。让 E ⊂Ω × Ω 是可测等价关系，即 E∈F⊗F 和 Ω 上的关系定义为 x ∼ y ⇔ ( x,y ) ∈ E 是重外向、对称和传递的。证明在 Ω 上有两个 σ - 费尔德 G 0 和 G 1，对于所有 µ，ν ∈ P ( F ) 、
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