NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

doi:10.1016/S0252-9602(13)60076-4

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1231-1242.doi: 10.1016/S0252-9602(13)60076-4

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

Á.G. HORVÁTH

Department of Geometry, Mathematical Institute, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

收稿日期:2012-05-03 修回日期:2013-04-03 出版日期:2013-09-20 发布日期:2013-09-20
作者简介:We rather denote in this paper the space of O-symmetric convex bodies by K0 as the space of convex bodies with centroid O.

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

Á.G. HORVÁTH

Department of Geometry, Mathematical Institute, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

Received:2012-05-03 Revised:2013-04-03 Online:2013-09-20 Published:2013-09-20
About author:We rather denote in this paper the space of O-symmetric convex bodies by K0 as the space of convex bodies with centroid O.

摘要/Abstract

摘要：

In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with the property that its pushforward by the thinness function is a probability measure of truncated normal distribution. Finally, we improve this method to find a measure satisfying some important properties in geometric measure theory.

关键词: Hausdorff metric, Borel, Dirac, Haar and Lebesgue-measure, space of convex bodies, metric space of norms

Abstract:

Key words: Hausdorff metric, Borel, Dirac, Haar and Lebesgue-measure, space of convex bodies, metric space of norms

中图分类号:

52A20

á.G. HORVáTH. NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS[J]. 数学物理学报(英文版), 2013, 33(5): 1231-1242.

á.G. HORVáTH. NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS[J]. Acta mathematica scientia,Series B, 2013, 33(5): 1231-1242.

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NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

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