NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS  

作　　者：Á.G.HORVÁTH 

机构地区：[1]Department of Geometry, Mathematical Institute, Budapest University of Technology and Economics

出　　处：《Acta Mathematica Scientia》2013年第5期1231-1242,共12页数学物理学报（B辑英文版）

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.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 

分 类 号：O211.3[理学—概率论与数理统计] O189.11[理学—数学]