Generalization of portmanteau theorem with respect to the pseudoweak convergence of random closed sets

Abstract

The main result of this paper is a theorem of portmanteau type for pseudoweak convergent sequences of capacity functionals for a sequence of random closed sets. For that purpose the classical Lebesgue integral had been substituted with a more general one, known as general pseudo-integral, and there is introduced the pseudoweak convergence of capacity functionals. A connection between weak convergence of a sequence of probability measures induced by the sequence of random closed sets and convergence of pseudo-integral with respect to the corresponding sequence of capacity functionals is given. © 2010 Society for Industrial and Applied Mathematics.