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

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.