Abstract
We further investigate (M)-property, an important structure characteristic of monotone measures. Some necessary and/or sufficient conditions of (M)-property are shown and some characteristics of (M)-property are described. It is shown that the restriction of a monotone measure to an atom of its own possesses (M)-property on this atom. By means of the (M)-property we characterize the equivalence among the Choquet integral, the pan-integral, the concave integral, and the Shilkret integral on atoms of monotone measures and obtain some special results. We also show a necessary and sufficient condition for the concave integral and the pan-integral to coincide on atoms of monotone measures.
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