Integral representation of coherent upper conditional prevision with respect to its associated Hausdorff outer measure: a comparison among the Choquet integral, the pan-integral and the concave integral. Issue 6 (18th August 2018)

• Record Type: Journal Article
• Authors: Doria, Serena; Dutta, Bapi; Mesiar, Radko
• Is Part Of: International journal of general systems. Volume 47:Issue 6(2018)
• Page Start: 569
• Page End: 592
• Publication Date: 2018-08-18
• Subjects: Coherent upper conditional prevision -- Hausdorff outer measure -- Choquet integral -- pan-integral -- concave integral; System theory -- Periodicals; 003
• DOI: 10.1080/03081079.2018.1473392
• Languages: English
• ISSNs: 0308-1079

Abstract

Abstract : In this paper, it is proven that the natural extensions of a submodular coherent upper conditional probability, defined a class S properly contained in the power set of Ω, coincide on the class of all bounded and upper S -measurable random variables. Moreover, it is proven that a coherent upper conditional prevision can be represented as the Choquet integral, the pan-integral and the concave integral with respect to its associated Hausdorff outer measureh s and, denoted by S the σ -field of allh s -measurable sets, all these integral representations agree with the Lebesgue integral on the class of all S -measurable random variables.