Facts from Convex Geometry

In this book, the more concrete examples of random sets are generated as unions of random systems of convex bodies. The quantitative description of such random sets is based on functionals of convex bodies which are particularly adapted to taking unions: they are additive. In Section 14.2 we collect the basic facts about the most important of these functionals, the rigid motion invariant intrinsic volumes, and their local counterparts, the curvature measures. In Section 14.4 we provide general information about additive functionals, as far as needed.