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Bogachev, V.L. (2006) Measure Theory. Springer, Berlin.

has been cited by the following article:

  • TITLE: Monotone Measures Defined by Pan-Integral

    AUTHORS: Peipei Wang, Minhao Yu, Jun Li

    KEYWORDS: Monotone Measure, Pan-Integral, Sugeno Integral, Choquet Integral, Shilkret Integral

    JOURNAL NAME: Advances in Pure Mathematics, Vol.8 No.6, June 20, 2018

    ABSTRACT: Given a pan-space and a nonnegative measurable function f on measurable space (X, A), the pan-integral of f with respect to monotone measure μ and pan-operation determines a new monotone measure on(X, A). Such the new monotone measure is absolutely continuous with respect to the monotone measure μ. We show that the new monotone measure preserves some important structural characteristics of the original monotone measures, such as continuity from below, subadditivity, null-additivity, weak null-additivity and (S) property. Since the pan-integral based on a pair of pan-operations covers the Sugeno integral (based on ) and the Shilkret integral (based on ), therefore, the previous related results for the Sugeno integral are covered by the results presented here, in the meantime, some special results related the Shilkret integral are also obtained.