Convex cores of measures on R d
- 1 May 2001
- journal article
- Published by Akademiai Kiado Zrt. in Studia Scientiarum Mathematicarum Hungarica
- Vol. 38 (1-4) , 177-190
- https://doi.org/10.1556/sscmath.38.2001.1-4.12
Abstract
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.Keywords
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