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Bibliography

Journal Article

Relationship between the concave integrals and the pan-integrals on finite spaces

Ouyang Y., Li J., Mesiar Radko

: Journal of Mathematical Analysis and Applications vol.424, 2 (2015), p. 975-987

: Monotone measure Minimal atom, Concave integral, Pan-integral, Minimal atom

: 10.1016/j.jmaa.2014.11.058

: http://library.utia.cas.cz/separaty/2015/E/mesiar-0441980.pdf

(eng): This study discusses the relationship between the concave integrals and the pan-integrals on finite spaces. The minimal atom of a monotone measure is introduced and some properties are investigated. By means of two important structure characteristics related to minimal atoms: minimal atoms disjointness property and subadditivity for minimal atoms, a necessary and sufficient condition is given that the concave integral coincides with the pan-integral with respect to the standard arithmetic operations + and on finite spaces. Following this result, we have shown that these two integrals coincide if the underlying monotone measure is subadditive.

: BA

2019-01-07 08:39