Home Measure games on pseudo-D-lattices
Article
Licensed
Unlicensed Requires Authentication

Measure games on pseudo-D-lattices

  • Anna Avallone EMAIL logo
Published/Copyright: November 30, 2017
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 67 Issue 6

Abstract

We prove linearity theorems for modular measures on pseudo-D-lattices (= lattice ordered pseudo-effect algebras) and we study the consequences for the core of measure games.

MSC 2010: Primary 28B05; Secondary 06C16
Keywords: pseudo-D-lattices; measures; linearity theorems

Dedicated to Professor Paolo de Lucia on the occasion of his 80th birthday

Communicated by Anatolij Dvurečenskij

References

[1] Aumann, R.—Shapley, L.: Values of Non-atomic Games, Princeton Univ. Press, Princeton, 1974.Search in Google Scholar

[2] Avallone, A.—Barbieri, G.—Vitolo, P.: Central elements in pseudo-D-lattices and Hahn decomposition theorem, Boll. Unione Mat. Ital. 9 (2010), 447–470.Search in Google Scholar

[3] Avallone, A.—Barbieri, G.—Vitolo, P.: Pseudo-D-lattices and Lyapunov measures, Rend. Circ. Mat. Palermo 62 (2013), 301–314.10.1007/s12215-013-0126-6Search in Google Scholar

[4] Avallone, A.—Barbieri, G.—Vitolo, P.—Weber, H.: Decomposition of pseudo-effect algebras and the Hammer-Sobczyk theorem, Order, to appear.10.1007/s11083-015-9380-xSearch in Google Scholar

[5] Avallone, A.—Basile, A.: On a linearity theorem for measures, Sci. Math. Japon. 10 (2004), 471–484.Search in Google Scholar

[6] Avallone, A.—De Simone, A.—Vitolo, P.: Extension of measures on pseudo-D-lattices, Math. Slovaca 66 (2016), 421–438.10.1515/ms-2015-0147Search in Google Scholar

[7] Avallone, A.—Vitolo, P.: Pseudo-D-lattices and separating points of measures, Fuzzy Sets and Systems 289 (2016), 43–63.10.1016/j.fss.2015.06.015Search in Google Scholar

[8] Avallone, A.—Vitolo, P.: Pseudo-D-lattices and topologies generated by measures, Ital. J. Pure Appl. Math. 29 (2012), 25–42.Search in Google Scholar

[9] Avallone, A.—Vitolo, P.: Lebesgue decomposition and Bartle-Dunford-Schwartz theorem in pseudo-D-lattices, Acta Math. Sci. Ser. B Engl. Ed. 33 (2013), 653–677.10.1016/S0252-9602(13)60028-4Search in Google Scholar

[10] Avallone, A.—Vitolo, P.: Lattice uniformities on pseudo-D-lattices, Math. Slovaca 62 (2012), 1019–1044.10.2478/s12175-012-0062-5Search in Google Scholar

[11] Baudot, R.: Non-commutative logic programming language NoClog. In: Symposium LICS, Santa Barbara, 2000, pp. 3–9.Search in Google Scholar

[12] Barbieri, G.: Lyapunov’s theorem for measures on D-posets, Internat. J. Theoret. Phys. 43 (2004), 1613–1623.10.1023/B:IJTP.0000048807.37145.ccSearch in Google Scholar

[13] Beltrametti, E. G.—Cassinelli, G.: The Logic of Quantum Mechanics, Addison-Wesley Publ. Co., Reading, Mass., 1981.Search in Google Scholar

[14] Bennett, M. K.—Foulis, D. J.: Effect algebras and unsharp quantum logics, Found. Phys.24 (1994), 1331–1352.10.1007/BF02283036Search in Google Scholar

[15] Birkhoff, G.: Lattice Theory. In: Amer. Math. Soc. Colloq. Publ., Vol. XXV, 1967.Search in Google Scholar

[16] Butnariu, D.—Klement, P.: Triangular Norm-based Measures and Games with Fuzzy Coalitions. Kluwer Academic Publishers, Dordrecht, 1993.10.1007/978-94-017-3602-2Search in Google Scholar

[17] Dvurečenskij, A.: New quantum structures. In: Handbook of Quantum Logic and Quantum Structures, Elsevier Sci. B. V., Amsterdam, 2007, pp. 1–53.10.1016/B978-044452870-4/50023-6Search in Google Scholar

[18] Dvurečenskij, A.—Vetterlein, T.: Pseudoeffect algebras. I. Basic properties, Internat. J. Theoret. Phys. 40 (2001), 685–701.10.1023/A:1015561420306Search in Google Scholar

[19] Dvurečenskij, A.—Vetterlein, T.: Pseudoeffect algebras. II. Group representations, Internat. J. Theoret. Phys. 40 (2001), 703–726.10.1023/A:1004192715509Search in Google Scholar

[20] Epstein, L. G.—Zhang, J.: Subjective probabilities on subjectively unambiguous events, Econometrica 69 (2001), 265–306.10.1111/1468-0262.00193Search in Google Scholar

[21] Foulis, D. J.—Pulmannová, S.—Vinceková, E.: Type decomposition of a pseudoeffect algebra, J. Aust. Math. Soc. 89 (2010), 335–358.10.1017/S1446788711001042Search in Google Scholar

[22] Georgescu, G.—Iorgulescu, A.: Pseudo-MV algebras, Mult.-Valued Log. 6 (2001), 95–135.Search in Google Scholar

[23] Hart, S.—Neyman, A.: Values of non-atomic vector measure games, J. Math. Econom. 17 (1988), 31–40.10.1016/0304-4068(88)90025-0Search in Google Scholar

[24] Jakubik, J.: Projectability and weak homogeneity of pseudo effect algebras, Czechoslovak Math. J. 59 (2009), 183–196.10.1007/s10587-009-0013-7Search in Google Scholar

[25] Marinacci, M.: A uniqueness theorem for convex-ranged probabilities Decis. Econom. Finance 23 (200), 121–132.10.1007/s102030070003Search in Google Scholar

[26] Marinacci, M.—Montrucchio, L. Subcalculus for set functions and cores of TU games, J. Math. Econom. 1071 (2002), 1–25.10.1016/S0304-4068(02)00080-0Search in Google Scholar

[27] Pulmannová, S.: Generalized Sasaki projections and Riesz ideals in pseudoeffect algebras, Internat. J. Theoret. Phys. 42 (2003), 1413–1423.10.1023/A:1025723811099Search in Google Scholar

[28] Weber, H.: Uniform lattices. I: A generalization of topological Riesz spaces and topological Boolean rings, Ann. Mat. Pura Appl. 160 (1991), 347–370.10.1007/BF01764134Search in Google Scholar

[29] Weber, H.: Uniform lattices. II: Order continuity and exhaustivity, Ann. Mat. Pura Appl. 165 (1993), 133–158.10.1007/BF01765846Search in Google Scholar

[30] Weber, H.: On modular functions, Funct. Approx. Comment. Math. 24 (1996), 35–52.Search in Google Scholar

[31] Weber, H.: Uniform lattices and modular functions, Atti Semin. Mat. Fis. Univ. Modena 47 (1999), 159–182.Search in Google Scholar

[32] Yun, S.—Yongming, L.—Maoyin, C.: Pseudo difference posets and pseudo Boolean D-posets, Internat. J. Theoret. Phys. 43 (2004), 2447–2460.10.1007/s10773-004-7710-7Search in Google Scholar

Received: 2016-4-29
Accepted: 2016-7-4
Published Online: 2017-11-30
Published in Print: 2017-11-27

© 2017 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  2. Paolo de Lucia
  4. Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
  6. A note on field-valued measures
  8. Topologies and uniformities on d0-algebras
  10. On some properties of 𝓙-approximately continuous functions
  12. Porous subsets in the space of functions having the Baire property
  14. Rademacher’s theorem in Banach spaces without RNP
  16. Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
  18. Measure games on pseudo-D-lattices
  20. On some properties of k-subadditive lattice group-valued capacities
  22. Lp Spaces in vector lattices and applications
  24. The Choquet integral with respect to fuzzy measures and applications
  26. A note on the range of vector measures
  28. Ideal convergent subsequences and rearrangements for divergent sequences of functions
  30. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
  32. A generalization of the exponential sampling series and its approximation properties
  34. Monotonicity and total boundedness in spaces of “measurable” functions
  36. Vector lattices in synaptic algebras
  38. Density, ψ-density and continuity
  40. Feather topologies
  42. On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
  44. Rate of convergence of empirical measures for exchangeable sequences
  46. On non-additive probability measures
  48. Equi-topological entropy curves for skew tent maps in the square
  50. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
https://doi.org/10.1515/ms-2017-0058
Keywords for this article
pseudo-D-lattices; measures; linearity theorems

Articles in the same Issue

  2. Paolo de Lucia
  4. Arcs, hypercubes, and graphs as quotients of projective Fraïssé limits
  6. A note on field-valued measures
  8. Topologies and uniformities on d0-algebras
  10. On some properties of 𝓙-approximately continuous functions
  12. Porous subsets in the space of functions having the Baire property
  14. Rademacher’s theorem in Banach spaces without RNP
  16. Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces
  18. Measure games on pseudo-D-lattices
  20. On some properties of k-subadditive lattice group-valued capacities
  22. Lp Spaces in vector lattices and applications
  24. The Choquet integral with respect to fuzzy measures and applications
  26. A note on the range of vector measures
  28. Ideal convergent subsequences and rearrangements for divergent sequences of functions
  30. Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting
  32. A generalization of the exponential sampling series and its approximation properties
  34. Monotonicity and total boundedness in spaces of “measurable” functions
  36. Vector lattices in synaptic algebras
  38. Density, ψ-density and continuity
  40. Feather topologies
  42. On disruptions of nonautonomous discrete dynamical systems in the context of their local properties
  44. Rate of convergence of empirical measures for exchangeable sequences
  46. On non-additive probability measures
  48. Equi-topological entropy curves for skew tent maps in the square
  50. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 18.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0058/html
Scroll to top button