等价耦合和总变异的一些对偶性结果

Pub Date : 2024-01-01 DOI:10.1214/24-ecp586

L. Pratelli, P. Rigo

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引用次数: 0

摘要

.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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Some duality results for equivalence couplings and total variation

. 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 ),

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