Convergence theorems for adapted sequences of random sets |
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| Authors: | Leszek Gasiński Nikolaos S. Papageorgiou |
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| Affiliation: | 1. Department of Mathematics, Pedagogical University of Cracow, Cracow, Poland;2. Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland;3. Department of Mathematics, Zografou Campus, National Technical University, Athens, Greece |
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| Abstract: | We consider random sets with values in a separable Banach space. We study set-valued amarts, L1-amarts, uniform amarts and submartingales. For all these classes of random sets, we prove convergence theorems in all main modes of set convergence (weak, Wijsman, Mosco, and Hausdorff). We also prove new convergence theorems for vector-valued subpramarts and pramarts. |
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| Keywords: | Random sets set convergence amarts submartingales support function distance function |
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