Limit theorems for unions of random closed sets

Molchanov I.

The book begins with the introduction of the basic tools and known results on random sets distributions and their weak convergence. Although the book is devoted to the study of limit theorems for unions. in Chapter 2 we present several results on Minkowski sums of random compact sets in the Euclidean space. In Chapter 3 we bring the notions of union stable and convex stable random closed sets. Their distributions are characterized in terms of the corresponding capacity or inclusion functionals. In Chapter 4 of 8 we prove limit theorems for scaled unions and convex hulls of random sets. Limit theorems for unions of special random sets and et cetera.