Previous |  Up |  Next

Article

Keywords:
effect algebra; Dieudonné theorem; modular measures; lattice group
Summary:
A version of Dieudonné theorem is proved for lattice group-valued modular measures on lattice ordered effect algebras. In this way we generalize some results proved in the real-valued case.
References:
[1] Avallone, A.: Separating points of measures on effect algebras. Mathematica Slovaca 20 (2006), 203-214. MR 2357812
[2] Avallone, A.: Cafiero and Nikodym boundedness theorem in effect algebras. Ital. J. Pure Appl. Math. 57 (2007), 2, 129-140. MR 2247423
[3] Barbieri, G.: On the Dieudonné theorem. Sci. Math. Japon. 70 (2009), 3, 279-284. MR 2562049
[4] Bennett, M. K., Foulis, D. J.: Effect algebras and unsharp quantum logics. Special issue dedicated to Constantin Piron on the occasion of his sixtieth birthday. Found. Phys. 24 (1994), 10, 1331-1352. DOI 10.1007/bf02283036 | MR 1304942
[5] Boccuto, A.: Dieudonné-type theorems for means with values in Riesz spaces. Tatra Mountains Math. Publ. 8 (1996), 9-42. MR 1475257
[6] Boccuto, A., Candeloro, D.: Some new results about Brooks-Jewett and Dieudonné-type theorems in (l)-groups. Kybernetika 46 (2010), 6, 1049-1060. MR 2797426
[7] Boccuto, A., Dimitriou, X.: Equivalence between limit theorems for lattice group-valued $k$-triangular set functions. Mediterr. J. Math. 4 (2018), Art. 174, 20 pp. DOI 10.1007/s00009-018-1222-9 | MR 3825621
[8] Butnariu, D., Klement, E. P.: Triangular norm-based measures and games with fuzzy coalitions. Theory and Decision Library. Series C: Game Theory, Mathematical Programming and Operations Research, 10. Kluwer Academic Publishers Group, Dordrecht 1993. DOI 10.1007/978-94-017-3602-2 | MR 2867321
[9] Chovanec, F., Kopka, F.: D-posets. Math. Slovaca 44 (1994), 1, 21-34. MR 1290269
[10] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer Academic Publishers, Bratislava 2000. DOI 10.1007/978-94-017-2422-7_1 | MR 1861369 | Zbl 0987.81005
[11] Epstein, L. G., Zhang, J.: Subjective probabilities on subjectively unambiguous events. Econometrica 69 (2001), 2, 265-306. DOI 10.1111/1468-0262.00193 | MR 1819756
[12] Fleischer, I., Traynor, T.: Equivalence of group-valued measures on an abstract lattice. Bull. Acad. Polon. Sci. Sci. Math. 28 (1980), 11-12, 549-556. MR 0628641
[13] Fremlin, D. H.: A direct proof of the Matthes-Wright integral extension theorem. J. London Math. Soc. 11 (1975), 2, 276-284. DOI 10.1112/jlms/s2-11.3.276 | MR 0380345
[14] Riečan, B., Neubrunn, T.: Integral, Measure and Ordering. Kluwer Acad. Publ./Ister Science, Dordrecht/Bratislavia 1997. DOI 10.1007/978-94-015-8919-2 | MR 1489521 | Zbl 0916.28001
Partner of
EuDML logo