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✦   LIBER   ✦

A Kinematic Formula and Moment Measures of Random Sets

✍ Scribed by M. Zähle

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
608 KB
Volume
149
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Relations for higher order m‐volume direction moment measures of motion invariant random sets in R^d^ and their intersections by planes are derived. As a fundamental tool a new kinematic formula for moments of Hausdorff measures is proved.

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## Abstract Let __X__ be a set of positive reach in the __d__‐dimensional Euclidean space. We present formulae for the integrals of the curvature measures of flat sections of __X__ with respect to all translations/Euclidean motions of the sectioning flat. We consider the (generalized) curvature mea