### 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.

Original language | English |
---|---|

Pages (from-to) | 177-190 |

Number of pages | 14 |

Journal | Studia Scientiarum Mathematicarum Hungarica |

Volume | 38 |

Issue number | 1-4 |

Publication status | Published - 2002 |

### Fingerprint

### 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

^{d}.

*Studia Scientiarum Mathematicarum Hungarica*,

*38*(1-4), 177-190.

**Convex cores of measures on ℝ ^{d}.** / Csiszár, I.; Matúš, F.

Research output: Contribution to journal › Article

^{d}',

*Studia Scientiarum Mathematicarum Hungarica*, vol. 38, no. 1-4, pp. 177-190.

^{d}. Studia Scientiarum Mathematicarum Hungarica. 2002;38(1-4):177-190.

}

TY - JOUR

T1 - Convex cores of measures on ℝd

AU - Csiszár, I.

AU - Matúš, F.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Convex sets in n dimensions

KW - Convex support

KW - Convolution

KW - Exponential family

KW - Lattice of faces

KW - Means of probabilities

UR - http://www.scopus.com/inward/record.url?scp=0010075422&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010075422&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0010075422

VL - 38

SP - 177

EP - 190

JO - Studia Scientiarum Mathematicarum Hungarica

JF - Studia Scientiarum Mathematicarum Hungarica

SN - 0081-6906

IS - 1-4

ER -