Coincidences of the Concave Integral and the Pan-Integral

Ouyang, Yao; Li, Jun; Mesiar, Radko

doi:10.3390/sym9060090

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Article

16 June 2017

9 Pages

Coincidences of the Concave Integral and the Pan-Integral

and

Faculty of Science, Huzhou Teacher’s College, Huzhou 313000, China

School of Sciences, Communication University of China, Beijing 100024, China

Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia

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Institute of Information Theory and Automation of the CAS, Pod Vodárenskou věží 4, 182 08 Prague, Czech Republic

Symmetry2017, 9(6), 90;https://doi.org/10.3390/sym9060090

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Abstract

In this note, we discuss when the concave integral coincides with the pan- integral with respect to the standard arithmetic operations + and ·. The subadditivity of the underlying monotone measure is one sufficient condition for this equality. We show also another sufficient condition, which, in the case of finite spaces, is necessary, too.

Keywords:

monotone measure; subadditivity; concave integral; pan-integral

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