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On some properties of submeasures on MV-algebras. (English) Zbl 1066.28009

The authors study a special kind of submeasures on an MV-algebra (so-called Dobrakov submeasures) and prove that in this case nonatomicity is equivalent to the Darboux property.

MSC:

28E10 Fuzzy measure theory
06D35 MV-algebras
03G12 Quantum logic
28A33 Spaces of measures, convergence of measures
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References:

[1] ČERNEK P.: Product of submeasures. Acta Math. Univ. Comenian. 40-41 (1982), 301-308. · Zbl 0945.03095
[2] ČERNEK P.: The least upper bound of the additive measures and integrals. Zb. Rad., Prir.-Math. 25 (1971), 21-24.
[3] CHANG C. C.: Algebraic analysis of many-valued logics. Trans. Amer. Math. Soc. 88 (1959), 467-490. · Zbl 0084.00704 · doi:10.2307/1993227
[4] DOBRAKOV I.: On submeasures I. Dissertationes Math. (Rozprawy Mat.) 112 (1974), 5-35. · Zbl 0292.28001
[5] DVUREČENSKIJ A.-PULMANNOVÁ S.: New Trends in Quantum Structures. Cluwer Acad. Publ./Ister Science, Dordrecht/Bratislava, 2000. · Zbl 0987.81005
[6] HALMOS P. R.: The range of a vector measure. Bull. Amer. Math. Soc. 54 (1948), 416-421. · Zbl 0033.05201 · doi:10.1090/S0002-9904-1948-09020-6
[7] KLIMKIN V. M.-SVISTULA M. G.: The Darboux property of non-additive set functions. Mat. Sb. 192 (2001), 41-50. · Zbl 1039.28002 · doi:10.1070/SM2001v192n07ABEH000578
[8] OLEJČEK V.: Darboux property of finitely additive measure on \(\delta\)-ring. Math. Slovaca 27 (1997), 195-201.
[9] RIEČAN B.: On the Dobrakov submeasure on fuzzy sets. Fuzzy Sets and Systems · Zbl 1061.28013 · doi:10.1016/j.fss.2004.07.004
[10] RIEČAN B.-NEUBRUNN T.: Integral, Measure, and Ordering. Kluwer Acad. Publ./Ister Science, Dordrecht/Bratislava, 1997. · Zbl 0916.28001
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