On the connectedness of a random closed set of a Euclidean space
Autor
Salamanca, Juan J.
Herrera, Jónatan
Rubio, Rafael M.
Editor
ElsevierFecha
2022Materia
Random closed setCapacity functional
Simplicial complex
Topology
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Our aim is to obtain a suitable characterization of certain topological properties of a random closed set through its capacity
functional. The main technique mixes two different fields: on the one hand, the abstract simplicial complex associated to a covering,
whose topology coincides with the topology of the original set thanks to the nerve theorem. On the other hand, the celebrated
Choquet-Kendall-Matheron theorem, which states that a random closed set is characterized by its capacity functional.
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Embargado hasta 30/08/2024