Atoms of weakly null-additive monotone measures and integrals

Authors:
Jun Li;Radko Mesiar;Endre Pap
Affiliations:
-;-;-
Venue:
Information Sciences: an International Journal
Year:
2014

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Abstract

In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by Pap. The calculation of the Sugeno integral and the Choquet integral over an atom is also presented, respectively. Similar results for recently introduced universal integral are also given. Following these results, it is shown that the Sugeno integral and the Choquet integral over an atom of monotone measure is maxitive linear and standard linear, respectively. Convergence theorems for the Sugeno integral and the Choquet integral over an atom of a monotone measure are also shown.