Acta mathematica scientia,Series B ›› 2013, Vol. 33 ›› Issue (5): 1231-1242.doi: 10.1016/S0252-9602(13)60076-4

• Articles • Previous Articles     Next Articles

NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS

Á.G. HORVÁTH   

  1. 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.

Abstract:

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.

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

CLC Number: 

  • 52A20
Trendmd