Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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

Information

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

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

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

Rights: Copyright © 2000 Institute of Mathematical Statistics

JOURNAL ARTICLE
55 PAGES


SHARE
Vol.28 • No. 2 • April 2000
Back to Top