Bivariate measure-inducing quasi-copulas

被引：1
作者：
Stopar, Nik [1 ,2 ]
机构：
[1] Univ Ljubljana, Fac Civil & Geodet Engn, Ljubljana, Slovenia
[2] Inst Math Phys & Mech, Ljubljana, Slovenia
来源：
FUZZY SETS AND SYSTEMS | 2024年 / 492卷
关键词：
Quasi-copula; Copula; Signed measure; Total variation norm; Infinite series;
D O I：
10.1016/j.fss.2024.109068
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
It is well known that every bivariate copula induces a positive measure on the Borel sigma-algebra on [0 , 1](2), but there exist bivariate quasi-copulas that do not induce a signed measure on the same sigma-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.
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页数：20
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