Jurečková, Mária; Chovanec, Ferdinand On some properties of submeasures on MV-algebras. (English) Zbl 1066.28009 Math. Slovaca 54, No. 2, 161-167 (2004). 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. Reviewer: Beloslav Riečan (Banská Bystrica ) Cited in 2 Documents MSC: 28E10 Fuzzy measure theory 06D35 MV-algebras 03G12 Quantum logic 28A33 Spaces of measures, convergence of measures Keywords:submeasure on MV-algebra; nonatomicity; Darboux property; Saks property PDFBibTeX XMLCite \textit{M. Jurečková} and \textit{F. Chovanec}, Math. Slovaca 54, No. 2, 161--167 (2004; Zbl 1066.28009) 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.