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Symmetry 2017, 9(6), 90;

Coincidences of the Concave Integral and the Pan-Integral

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
Institute of Information Theory and Automation of the CAS, Pod Vodárenskou věží 4, 182 08 Prague, Czech Republic
Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 28 May 2017 / Revised: 8 June 2017 / Accepted: 13 June 2017 / Published: 16 June 2017
Full-Text   |   PDF [222 KB, uploaded 20 June 2017]


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. View Full-Text
Keywords: monotone measure; subadditivity; concave integral; pan-integral monotone measure; subadditivity; concave integral; pan-integral
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Ouyang, Y.; Li, J.; Mesiar, R. Coincidences of the Concave Integral and the Pan-Integral. Symmetry 2017, 9, 90.

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