Abstract
This work studies the connectedness of a random closed set in a Euclidean space. The well-known Choquet-Kendall-Matheron theorem states that a random closed set is characterized by its capacity functional. Consequently, any topological property must be also determined by such functional. In this work we consider connectedness. Under mild conditions, this property can be determined by taking into account only the capacity functional valued on predetermined finite families of compact and convex sets. The technique is based on the construction of an abstract simplicial complex associated with a cover of the support of the random closed set. We consider a new application in Probability, where we are able to approximate some probability computations.
By project PGC2018-098623-B-I00.
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Salamanca, J.J. (2021). Discussions on the Connectedness of a Random Closed Set. In: Denœux, T., Lefèvre, E., Liu, Z., Pichon, F. (eds) Belief Functions: Theory and Applications. BELIEF 2021. Lecture Notes in Computer Science(), vol 12915. Springer, Cham. https://doi.org/10.1007/978-3-030-88601-1_28
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DOI: https://doi.org/10.1007/978-3-030-88601-1_28
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