Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 479-488 (2006)

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Crofton measures in polytopal Hilbert geometries

Rolf Schneider

Mathematisches Institut, Albert-Ludwigs-Universität; Eckerstr. 1, 79104 Freiburg i.Br., Germany

Abstract: The Hilbert geometry in an open bounded convex set in ${\mathbb R}^n$ is a classical example of a projective Finsler space. We construct explicitly a positive measure on the space of lines in a polytopal Hilbert geometry which yields an integral geometric representation of Crofton type for the Holmes-Thompson area of hypersurfaces.

Classification (MSC2000): 53C60; 53C65, 52B11

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Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.

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