Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 2, pp. 479488 (2006) 

Crofton measures in polytopal Hilbert geometriesRolf SchneiderMathematisches Institut, AlbertLudwigsUniversität; Eckerstr. 1, 79104 Freiburg i.Br., Germanyemail: rolf.schneider@math.unifreiburg.de 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 HolmesThompson area of hypersurfaces. Classification (MSC2000): 53C60; 53C65, 52B11 Full text of the article:
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