On support measures in minkowski spaces and contact distributions in stochastic geometry

Authors
Citation
D. Hug et G. Last, On support measures in minkowski spaces and contact distributions in stochastic geometry, ANN PROBAB, 28(2), 2000, pp. 796-850
Citations number
43
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
28
Issue
2
Year of publication
2000
Pages
796 - 850
Database
ISI
SICI code
0091-1798(200004)28:2<796:OSMIMS>2.0.ZU;2-I
Abstract
This paper is concerned with contact distribution functions of a random clo sed set Xi = U-n=1(infinity) Xi (n) in 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 c onvex gauge body (structuring element) that contains the origin in its inte rior. Support measures with respect to such distances will be introduced an d extended to sets in the local convex ring. These measures will then be us ed 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 ge neral nonstationary setting Only the final section deals with the stationar y case.