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The symmetric Choquet integral with respect to Riesz-space-valued capacities

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Abstract

A definition of “Šipoš integral” is given, similarly to [3], [5], [10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, via Vanvitelli, 1-06123, Perugia, Italy

    Antonio Boccuto

  2. Katedra Matematiky, Fakulta Prírodných Vied, Univerzita Mateja Bela, Tajovského 40, SK-974 01, Banská Bystrica, Slovakia

    Beloslav Riečan

Authors
  1. Antonio Boccuto
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  2. Beloslav Riečan
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Correspondence to Antonio Boccuto.

Additional information

This paper was supported by the cooperation project between Slovak Academy of Sciences (S.A.V.) and Italian National Council of Researches (C.N.R.)

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Boccuto, A., Riečan, B. The symmetric Choquet integral with respect to Riesz-space-valued capacities. Czech Math J 58, 289–310 (2008). https://doi.org/10.1007/s10587-008-0017-8

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  • DOI: https://doi.org/10.1007/s10587-008-0017-8

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