Open Access
April 2000 On support measures in Minkowski spaces and contact distributions in stochastic geometry
Daniel Hug, Günter Last
Ann. Probab. 28(2): 796-850 (April 2000). DOI: 10.1214/aop/1019160261


This paper is concerned with contact distribution functions of a random closed set $\Xi=\Bigcup_{n=1}^\infty \Xi_n$ in $\mathbb{R}^d$, where the $\Xi_n$ are assumed to be random nonempty convex bodies. These distribution functions are defined here in terms of a distance function which is associated with a strictly convex gauge body (structuring element) that contains the origin in its interior. Support measures with respect to such distances will be introduced and extended to sets in the local convex ring.These measures will then be used in a systematic way to derive and describe some of the basic properties of contact distribution functions. Most of the results are obtained in a general nonstationary setting.Only the final section deals with the stationary case.


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Daniel Hug. Günter Last. "On support measures in Minkowski spaces and contact distributions in stochastic geometry." Ann. Probab. 28 (2) 796 - 850, April 2000.


Published: April 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60006
MathSciNet: MR1782274
Digital Object Identifier: 10.1214/aop/1019160261

Primary: 52A21 , 60D05 , 60G57
Secondary: 46B20 , 52A20 , 52A22 , 53C65 , 60G55

Keywords: contact distribution function , Germ-grain model , marked point process , Minkowski space , Palm probabilities , randommeasure , Stochastic geometry , support (curvature) measure

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 2 • April 2000
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