Introduction to Random Closed Sets and to Semi-Continuous Random Functions

Abstract

This chapter recalls the construction and the main properties of random closed sets: i) The Choquet topology, for the closed sets of a space E, enables us to build a probability space of closed random sets, characterized by their Choquet capacity. ii) From the same approach extended to upper or lower semi continuous numerical functions, it is possible to build random functions for which the supremum or the infimum of its values inside a compact set K is a random variable.