Abstract
This note studies the coincidences among the Choquet, concave and pan-integral in the setting of an ordered pair of monotone measures. We further investigate some properties of the minimal atoms and (M)-property of monotone measures, and optimal measures. By using these properties we present several sufficient and/or necessary conditions of coincidences among these three integrals, in the context relating to two monotone measures. These generalized versions, as special cases, cover respectively the coincidences in the usual sense among the pan-integral, the Choquet integral, and the concave integral on finite spaces.
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