Normally Distributed Probability Measure on the Metric Space of Norms |
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Authors: | Á .G. HORVÁ TH |
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Affiliation: | Department of Geometry, Mathematical Institute, Budapest University of Technology and Economics, H-1521 Budapest, Hungary |
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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. |
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Keywords: | Hausdorff metric Borel Dirac Haar and Lebesgue-measure space of convex bodies metric space of norms |
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