Convex cores of measures on Rd

被引：17

作者：

Csiszár, I

Matús, F

机构：

[1] Mta Renyi Alfred Matemat Kutatointezete, H-1364 Budapest, Hungary

[2] Acad Sci Czech Republ, Inst Informat Theory & Automat, CZ-18208 Prague, Czech Republic

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2001年 / 38卷

关键词：

convex support; convex sets in n dimensions; lattice of faces; means of probabilities; convolution; exponential family;

D O I：

10.1556/SScMath.38.2001.1-4.12

中图分类号：

O1 [数学];

学科分类号：

0701 [数学]; 070101 [基础数学];

摘要：

We define the convex core of a finite Borel measure Q on R-d as the intersection of all convex Borel sets C with Q(C) = Q(R-d). It consists exactly of means of probability measures dominated by Q. Geometric and measure-theoretic properties of convex cores are studied, including behaviour under certain operations on measures. Convex cores are characterized as those convex sets that have at most countable number of faces.

引用

页码：177 / 190

页数：14