7 research outputs found

    Autocontinuity and convergence theorems for the Choquet integral

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    Our aim is to provide some convergence theorems for the Choquet integral with respect to various notions of convergence. For instance, the dominated convergence theorem for almost uniform convergence is related to autocontinuous set functions. Autocontinuity can also be related to convergence in measure, strict convergence or mean convergence. Whereas the monotone convergence theorem for almost uniform convergence is related to monotone autocontinuity, a weaker version than autocontinuity.

    Generalized Measure Theory

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    On Properties of the Choquet Integral of Interval-Valued Functions

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    Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of interval-valued functions. We also discuss convergence in the (C) mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem for the Choquet integral of measurable interval-valued functions

    測度収束関数列の非線形積分のpp次収束性 (関数空間の一般化とその周辺)

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    Choquet積分のVitali型収束定理 (関数空間の構造とその周辺)

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    As the consumptive demand for water approaches its availability, proper resource management becomes imperative. The authors present the proposal for state regulation of consumptive uses of water contained in Chapter Two of the Draft of the Model Water Code
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