Geodesic
Generalization of Portmanteau Theorem with Respect to the Pseudoweak Convergence of Random Closed Sets
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 1, pp. 97-115

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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.
Keywords: pseudo-operations, pseudo-integral, random closed set, capacity functional, pseudoweak convergence.
Mots-clés : portmanteau theorem 
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     title = {Generalization of {Portmanteau} {Theorem} with {Respect} to the {Pseudoweak} {Convergence} of {Random} {Closed} {Sets}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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T. Grbić; E. Pap. Generalization of Portmanteau Theorem with Respect to the Pseudoweak Convergence of Random Closed Sets. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 1, pp. 97-115. http://geodesic.mathdoc.fr/item/TVP_2009_54_1_a5/