Convex cores of measures on ℝd

I. Csiszár, F. Matúš

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We define the convex core of a finite Borel measure Q on ℝd as the intersection of all convex Borel sets C with Q(C) = Q(ℝd). 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.

Original languageEnglish
Pages (from-to)177-190
Number of pages14
JournalStudia Scientiarum Mathematicarum Hungarica
Volume38
Issue number1-4
Publication statusPublished - 2002

Fingerprint

Convex Sets
Borel Set
Borel Measure
Probability Measure
Countable
Intersection
Face

Keywords

  • Convex sets in n dimensions
  • Convex support
  • Convolution
  • Exponential family
  • Lattice of faces
  • Means of probabilities

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Convex cores of measures on ℝd. / Csiszár, I.; Matúš, F.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 38, No. 1-4, 2002, p. 177-190.

Research output: Contribution to journalArticle

Csiszár, I. ; Matúš, F. / Convex cores of measures on ℝd. In: Studia Scientiarum Mathematicarum Hungarica. 2002 ; Vol. 38, No. 1-4. pp. 177-190.
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