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Effect algebras with the subsequential interpolation property

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Abstract

We prove Brooks–Jewett, Vitali–Hahn–Saks and NikodymBoundedness theorems for modular measures on lattice-ordered effect algebras with the subsequential interpolation property.

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References

  • Avallone A (2001) Lattice uniformities on orthomodular structures.Math Slovaca 51(4):403–419

    MATH  MathSciNet  Google Scholar 

  • Avallone A (2006) Cafiero and Nikodym boundedness theorems in effectalgebras. Ital J Pure Appl Math 20:203–214

    MATH  MathSciNet  Google Scholar 

  • Avallone A, Basile A (2003) On a Marinacci uniqueness theorem formeasures. J Math Anal Appl 286(2):378–390

    Article  MATH  MathSciNet  Google Scholar 

  • Avallone A, Barbieri G, Vitolo P (2003) Hahn decomposition of modular measures and applications. Annal Soc Math Polon Series 1:Comment Math XLIII, 149–168

    MathSciNet  Google Scholar 

  • Barbieri G (2001) A note on fuzzy measures. J ElectricalEng 52:67–70

    MATH  Google Scholar 

  • Bennett MK, Foulis DJ (1994) Effect algebras and unsharp quantumlogics. Found Phys 24(10):1331–1352

    Article  MathSciNet  Google Scholar 

  • Beltrametti EG, Cassinelli G (1981) The logic of quantum mechanics.Addison-Wesley, Reading

    Google Scholar 

  • Butnariu D, Klement P (1993) Triangular norm-based measures andgames with fuzzy coalitions. Kluwer, Dordrecht

    Google Scholar 

  • D’Andrea AB, de Lucia P (1991) The Brooks–Jewett theorem on anorthomodular lattice. J Math Anal Appl 154:507–522

    Article  MATH  MathSciNet  Google Scholar 

  • D’Andrea AB, de Lucia P, Morales P (1991) The Lebesgue decompositiontheorem and the Nikodym convergence theorem on an orthomodularposet. Atti Sem Mat Fis Univ Modena 39:73–94

    MATH  MathSciNet  Google Scholar 

  • de Lucia P, Pap E (1995a) Noncommutative version of Nikodymboundedness theorem for uniform space valued functions. Int JTheor Phys 34(7):991–993

    Google Scholar 

  • de Lucia P, Pap E (1995b) Nikodym convergence theorem for uniformspace valued functions defined on D-posets. Math Slovaca45(4):367–376

    MATH  MathSciNet  Google Scholar 

  • Dvurecenskij A (1996) A note on Nikodym boundedness theorem. TatraMount Math Publ 8:229–238

    MATH  MathSciNet  Google Scholar 

  • Dvurecenskij A, Pulmannova S (2000) New trends in quantumstructures. Kluwer, Dordrecht

    Google Scholar 

  • Epstein LG, Zhang J (2001) Subjective probabilities on subjectivelyunambiguous events. Econometrica 69(2):265–306

    Article  MATH  MathSciNet  Google Scholar 

  • Freniche FJ (1984) The Vitali-Hahn-Saks theorem for Boolean algebraswith the Subsequential Interpolation Property. Proc Am Math Soc92:362–366

    Article  MATH  MathSciNet  Google Scholar 

  • Hamhalter J (1997) Nikodym boundedness theorem for von Neumannalgebras. Tatra Mount Math Publ 10:179–181

    MATH  MathSciNet  Google Scholar 

  • Hejcman J (1959) Boundedness in uniform spaces and topologicalgroups. Czech Math J 9:544–563

    MathSciNet  Google Scholar 

  • Kothe G (1983) Topological vector spaces. Springer, Heidelberg

    Google Scholar 

  • Weber H (1986) Compactness in spaces of group-valued contents, theVitali-Hahn-Saks theorem and Nikodym’s boundedness theorem. RockyMount J Math 16:253–275

    Article  MATH  Google Scholar 

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Correspondence to Anna Avallone.

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Supported by G.N.A.M.P.A.

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Avallone, A., Vitolo, P. Effect algebras with the subsequential interpolation property. Soft Comput 12, 559–565 (2008). https://doi.org/10.1007/s00500-007-0228-1

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