Densities for stationary random sets and point processes

Abstract

For certain stationary random sets X , densities D φ ( X ) of additive functionals φ are defined and formulas for are derived when K is a compact convex set in . In particular, for the quermassintegrals and motioninvariant X , these formulas are in analogy with classical integral geometric formulas. The case where X is the union set of a Poisson process Y of convex particles is considered separately. Here, formulas involving the intensity measure of Y are obtained.