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International Conference Series on Soft Methods in Probability and Statistics

SMPS 2018: Uncertainty Modelling in Data Science pp 208–215Cite as

Choquet Theorem for Random Sets in Polish Spaces and Beyond

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 832))

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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Author information

Authors and Affiliations

  1. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Gijón, Spain

    Pedro Terán

Authors
  1. Pedro Terán
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Correspondence to Pedro Terán .

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Editors and Affiliations

  1. CNRS, Heudiasyc, Sorbonne universités, Université de technologie de Compiègne, Compiegne, France

    Sébastien Destercke

  2. CNRS, Heudiasyc, Sorbonne universités, Université de technologie de Compiègne, Compiegne, France

    Thierry Denoeux

  3. Department of Statistics and Operational Research and Mathematics Didactics, University of Oviedo, Oviedo, Asturias, Spain

    María Ángeles Gil

  4. Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland

    Przemyslaw Grzegorzewski

  5. Department of Stochastic Methods, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Olgierd Hryniewicz

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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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