Normally distributed probability measure on the metric space of norms

Details Normally distributed probability measure on the metric space of norms Normally distributed probability measure on the metric space of norms

2011-05-19

arxiv.org/abs/1105.3809v3

Mathematics

Probability

13 pages

Scientific paper

In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies, which pushforward by the thinness mapping produces a probability measure of truncated normal distribution on the interval of its range. Improving the construction we give another (more complicated) one with the following additional properties; the neighborhoods have positive measure, the set of polytopes has zero measure and the set of smooth bodies has measure 1, respectively.

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