Abstract
A fundamental long-standing problem in the theory of random sets is concerned with the possible characterization of the distributions of random closed sets in Polish spaces via capacities. Such a characterization is known in the locally compact case (the Choquet theorem) in two equivalent forms: using the compact sets and the open sets as test sets. The general case has remained elusive. We solve the problem in the affirmative using open test sets.
Dedicated to the memory of my mother Ángeles Vicenta Agraz Viván, who passed away on March 21st, 2017. Research in this paper was partially funded by Asturias’s Consejería de Economía y Empleo (FC-15-GRUPIN14-101) and by Spain’s Ministerio de Economía y Competitividad (MTM2015–63971–P).
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Terán, P. (2019). Choquet Theorem for Random Sets in Polish Spaces and Beyond. In: Destercke, S., Denoeux, T., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Uncertainty Modelling in Data Science. SMPS 2018. Advances in Intelligent Systems and Computing, vol 832. Springer, Cham. https://doi.org/10.1007/978-3-319-97547-4_27
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DOI: https://doi.org/10.1007/978-3-319-97547-4_27
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