On the equivalence of the Choquet, pan- and concave integrals on finite spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00477091" target="_blank" >RIV/67985556:_____/17:00477091 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.06.086" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.06.086</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.06.086" target="_blank" >10.1016/j.jmaa.2017.06.086</a>
Alternative languages
Result language
angličtina
Original language name
On the equivalence of the Choquet, pan- and concave integrals on finite spaces
Original language description
In this paper we introduce the concept of maximal cluster of minimal atoms on monotone measure spaces and by means of this new concept we continue to investigate the relation between the Choquet integral and the pan-integral on finite spaces. It is proved that the (M)-property of a monotone measure is a sufficient condition that the Choquet integral coincides with the pan-integral based on the usual addition + and multiplication. Thus, combining our recent results, we provide a necessary and sufficient condition that the Choquet integral is equivalent to the pan-integral on finite spaces. Meanwhile, we also use the characteristics of minimal atoms of monotone measure to present another necessary and sufficient condition that these two kinds of integrals are equivalent on finite spaces. The relationships among the Choquet integral, the pan-integral and the concave integral are summarized.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
456
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
151-162
UT code for WoS article
000407667900008
EID of the result in the Scopus database
2-s2.0-85023597858