Valuations and Boolean Models

Abstract

Valuations, as additive functionals, allow various applications in Stochastic Geometry, yielding mean value formulas for specific random closed sets and processes of convex or polyconvex particles. In particular, valuations are especially adapted to Boolean models, the latter being the union sets of Poisson particle processes. In this chapter, we collect mean value formulas for scalar- and tensor-valued valuations applied to Boolean models under quite general invariance assumptions.