Empirical associated functionals and their application to the analysis of stable random sets and processes (Q1175852)

Let \(A\) be a random closed set in a locally compact separable space \(E\), and \(A_1,\ldots,A_n\) be a sample of i.i.d. copies of \(A\). The author gives various conditions ensuring the a.s. uniform convergence (in analogy to Glivenko-Cantelli's classical theorem) of the empirical hitting function \(T_n^*(K)=(1/n)\sum_{i=1}^ n 1_{A_i\cap K\neq\emptyset}\) to the hitting function of \(T(K)=\mathbb{P}(A\cap K\neq\emptyset)\) of \(A\) both acting on the class of compact sets in \(E\).