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Monotone Measures Defined by Pan-Integral

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Document pages: 13 pages

Abstract: Given a pan-space  and a nonnegativemeasurable function f on measurablespace (X, A), the pan-integral of f with respect to monotone measure μ andpan-operation  determines a newmonotone measure  on (X, A). Such the new monotone measure  is absolutelycontinuous with respect to the monotone measure μ. We show that the new monotone measure preserves some importantstructural characteristics of the original monotone measures, such ascontinuity from below, subadditivity, null-additivity, weak null-additivity and(S) property. Since the pan-integral based on a pair of pan-operations  covers the Sugenointegral (based on ) and the Shilkretintegral (based on ), therefore, the previous related results for the Sugenointegral are covered by the results presented here, in the meantime, somespecial results related the Shilkret integral are also obtained.

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