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Absolute curvature measures for unions of sets with positive reach

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Jan Rataj
Jan Rataj
Affiliation:
Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic.
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Abstract

Absolute curvature measures for locally finite unions of sets with positive reach are introduced, extending the definition of Zähle [13] by taking into account the absolute value of the index function. It is shown that this definition differs from that of Matheron [5] and Schneider [12]. An intersection formula of Crofton type for absolute curvature measures is proved. The role of absolute curvature measures in geometric statistics is illustrated by an example.

MSC classification

Secondary: 52A22: Random convex sets and integral geometry
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 33 - 44
Copyright
Copyright © University College London 2002

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