Regularities of Riesz space-valued non-additive measures with applications to convergence theorems for Choquet integrals

DOI10.1016/J.FSS.2009.06.001zbMath1183.28032OpenAlexW2054441056MaRDI QIDQ2270243

Jun Kawabe

Publication date: 18 March 2010

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.fss.2009.06.001

zbMATH Keywords

Riesz space-valued non-additive measuretotal continuitymultiple Egoroff propertyregularity of measuresasymptotic null-additivity

Mathematics Subject Classification ID

Fuzzy measure theory (28E10)

Related Items (5)

Atoms of weakly null-additive monotone measures and integrals ⋮ Metrizability of the Lévy topology on the space of nonadditive measures on metric spaces ⋮ The continuity and compactness of Riesz space-valued indirect product measures ⋮ Nonadditive measures and nonlinear integrals —focusing on a theoretical aspect— ⋮ Regularity of fuzzy measures on complete and separable metric spaces

Cites Work

• The Choquet integral in Riesz space
• The Egoroff theorem for non-additive measures in Riesz spaces
• The Egoroff property and the Egoroff theorem in Riesz space-valued non-additive measure theory
• Regularity and Lusin's theorem for Riesz space-valued fuzzy measures
• Continuity and compactness of the indirect product of two non-additive measures
• A further investigation for fuzzy measures on metric spaces
• Regular fuzzy measure and representation of comonotonically additive functional
• Lusin's theorem on fuzzy measure spaces
• The Alexandroff theorem for Riesz space-valued non-additive measures
• Fuzzy regular measures on topological spaces
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