𝔖 Bobbio Scriptorium
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Curvature Measures and Random Sets, I

✍ Scribed by M. Zähle

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
668 KB
Volume
119
Category
Article
ISSN
0025-584X

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📜 SIMILAR VOLUMES

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Let us denote by C p ( K , .), r E {O,. . . , d -1)1 the curvature measures of a convex body K in the Euclidean space Ed with d 1. 2. According to Lebesgue's decomposition theorem the curvature measure of order r of K, C,(K, s), can be written as the sum of an absolutely continuous measure, C:(K, .)

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## 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.