Isometries of probability measures with respect to the total variation distance

被引：7

作者：

Dolinar, Gregor ^{[1
,2
]}

Kuzma, Bojan ^{[2
,3
,4
]}

Mitrovic, Dorde ^{[3
]}

机构：

[1] Univ Ljubljana, Fac Elect Engn, Trzaska Cesta 25, SI-1000 Ljubljana, Slovenia

[2] IMFM, Jadranska Cesta 19, SI-1000 Ljubljana, Slovenia

[3] Univ Primorska, Glagoljaska 8, SI-6000 Koper, Slovenia

[4] Moscow Ctr Fundamental & Appl Math, Moscow 119991, Russia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 507卷 / 02期

关键词：

Total variation distance; Distribution function; Isometry; SPACE;

D O I：

10.1016/j.jmaa.2021.125829

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize surjective isometries of the total variation distance between various subsets of Borel probability measures. In the case when isometrics are w*-continuous or in the case when their domain consists of measures which are absolutely continuous with respect to a fixed measure, such isometrics are push-forwards, i.e., compositum of a measure with a bijection. When the domain consists of all Borel probability measures, their classification is more involved. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：15

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