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Symmetry
Volume 9
Issue 6
10.3390/sym9060090
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Article

Coincidences of the Concave Integral and the Pan-Integral

by
Yao Ouyang
1,*,
Jun Li
2 and
Radko Mesiar
3,4
1
Faculty of Science, Huzhou Teacher’s College, Huzhou 313000, China
2
School of Sciences, Communication University of China, Beijing 100024, China
3
Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia
4
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.
Symmetry 2017, 9(6), 90; https://doi.org/10.3390/sym9060090
Submission received: 28 May 2017 / Revised: 8 June 2017 / Accepted: 13 June 2017 / Published: 16 June 2017
Versions Notes

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 monotone measure; subadditivity; concave integral; pan-integral

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MDPI and ACS Style

Ouyang, Y.; Li, J.; Mesiar, R. Coincidences of the Concave Integral and the Pan-Integral. Symmetry 2017, 9, 90. https://doi.org/10.3390/sym9060090

AMA Style

Ouyang Y, Li J, Mesiar R. Coincidences of the Concave Integral and the Pan-Integral. Symmetry. 2017; 9(6):90. https://doi.org/10.3390/sym9060090

Chicago/Turabian Style

Ouyang, Yao, Jun Li, and Radko Mesiar. 2017. "Coincidences of the Concave Integral and the Pan-Integral" Symmetry 9, no. 6: 90. https://doi.org/10.3390/sym9060090

APA Style

Ouyang, Y., Li, J., & Mesiar, R. (2017). Coincidences of the Concave Integral and the Pan-Integral. Symmetry, 9(6), 90. https://doi.org/10.3390/sym9060090

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