Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 424, Issue 2, Pages 975-987Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.11.058
Keywords
Monotone measure; Concave integral; Pan-integral; Minimal atom; Minimal atoms disjointness property
Categories
Funding
- National Natural Science Foundation of China [11371332]
- [APVV-0073-10]
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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 sub-additive. (C) 2014 Elsevier Inc. All rights reserved.
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