Kybernetika 55 no. 5, 870-878, 2019

A Dieudonné theorem for lattice group-valued measures

Giuseppina BarbieriDOI: 10.14736/kyb-2019-5-0870


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.


effect algebra, Dieudonné theorem, lattice group, modular measures


28A12, 28A33, 28B15


  1. A. Avallone: Separating points of measures on effect algebras. Mathematica Slovaca 20 (2006), 203-214.   CrossRef
  2. A. Avallone: Cafiero and Nikodym boundedness theorem in effect algebras. Ital. J. Pure Appl. Math. 57 (2007), 2, 129-140.   CrossRef
  3. G. Barbieri: On the Dieudonné theorem. Sci. Math. Japon. 70 (2009), 3, 279-284.   CrossRef
  4. M. K. Bennett and D. J. Foulis: 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
  5. A. Boccuto: Dieudonné-type theorems for means with values in Riesz spaces. Tatra Mountains Math. Publ. 8 (1996), 9-42.   CrossRef
  6. A. Boccuto and D. Candeloro: Some new results about Brooks-Jewett and Dieudonné-type theorems in (l)-groups. Kybernetika 46 (2010), 6, 1049-1060.   CrossRef
  7. A. Boccuto and X. Dimitriou: 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
  8. D. Butnariu and E. P. Klement: 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
  9. F. Chovanec and F. K\^opka: D-posets. Math. Slovaca 44 (1994), 1, 21-34.   CrossRef
  10. A. Dvurečenskij and S. Pulmannová: New Trends in Quantum Structures. Kluwer Academic Publishers, Bratislava 2000.   DOI:10.1007/978-94-017-2422-7\_1
  11. L. G. Epstein and J. Zhang: Subjective probabilities on subjectively unambiguous events. Econometrica 69 (2001), 2, 265-306.   DOI:10.1111/1468-0262.00193
  12. I. Fleischer and T. Traynor: Equivalence of group-valued measures on an abstract lattice. Bull. Acad. Polon. Sci. Sci. Math. 28 (1980), 11-12, 549-556.   CrossRef
  13. D. H. Fremlin: A direct proof of the Matthes-Wright integral extension theorem. J. London Math. Soc. 11 (1975), 2, 276-284.   CrossRef
  14. B. Riečan and T. Neubrunn: Integral, Measure and Ordering. Kluwer Acad. Publ./Ister Science, Dordrecht/Bratislavia 1997.   DOI:10.1007/978-94-015-8919-2