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
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
收藏
页码:177 / 190
页数:14
相关论文
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[2]
CSISZAR I, 2000, P 2000 INT S INF THE
[3]
Rockafellar RT, 1970, PRINCETON MATH SERIE, V28
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Ziegler G., 1995, GRADUATE TEXTS MATH, V152