Acta mathematica scientia, Series B >
LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES
Received date: 2011-11-17
Online published: 2013-05-20
Let L be a pseudo-D-lattice. We prove that the exhaustive lattice uniformities on L which makes the operations of L uniformly continuous form a Boolean algebra isomorphic to the centre of a suitable complete pseudo-D-lattice associated to L. As a consequence, we obtain decomposition theorems—such as Lebesgue and Hewitt–Yosida decompositions—and control theorems—such as Bartle–Dunford–Schwartz and Rybakov theorems—for modular
measures on L.
Anna AVALLONE , Paolo VITOLO . LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 653 -677 . DOI: 10.1016/S0252-9602(13)60028-4
[1] Bennet M K, Foulis D J. Effect algebras and unsharp quantum logics. Found Phys, 1994, 24(10): 1331–1352
[2] Kˆopka F, Chovanec F. D-posets. Mathematica Slovaca, 1994, 44: 21–34
[3] Dvureˇcenskij A, Pulmannov´a S. New Trends in Quantum Structures. Dordrecht: Kluwer Academic Publishers,
2000
[4] Butnariu D, Klement P. Triangular Norm-based Measures and Games with Fuzzy Coalitions. Dordrecht: Kluwer Academic Publishers, 1993
[5] Epstein L G,Zhang J. Subjective probabilities on subjectively unambiguous events. Econometrica, 2001, 69(2): 265–306
[6] Dvureˇcenskij A, Vetterlein T. Pseudoeffect algebras. I. Basic properties. International Journal of Theoretical
Physics, 2001, 40(3): 685–701
[7] Georgescu G, Iorgulescu A. Pseudo-MV algebras: G C Moisil memorial issue. Mult.-Valued Log, 2001, 6(1/2): 95–135
[8] Dvureˇcenskij A. New quantum structures//Engesser K, Gabbay D M, Lehmann D. Handbook of quantum logic and quantum structures. Elsevier, 2007
[9] Bandot R. Non-commutative programming language. Santa Barbara: Symposium LICS, 2000: 3–9
[10] Dvureˇcenskij A. Central elements and Cantor–Bernstein theorem for pseudo-effect algebras. Journal of the
Australian Mathematical Society, 2003, 74: 121–143
[11] Dvureˇcenskij A, Vetterlein T. Congruences and states on pseudoeffect algebras. Found Phys Lett, 2001, 14(5): 425–446
[12] Dvureˇcenskij A, Vetterlein T. Pseudoeffect algebras. II. Group representations. International Journal of
Theoretical Physics, 2001, 40(3): 703–726
[13] Pulmannov´a S. Generalized Sasaki projections and Riesz ideals in pseudoeffect algebras. International Journal of Theoretical Physics, 2003, 42(7): 1413–1423
[14] Yun S, Yongming L, Maoyin C. Pseudo difference posets and pseudo Boolean D-posets. Internat J Theoret
Phys, 2004, 43(12): 2447–2460
[15] Avallone A, Vitolo P. Lattice uniformities on effect algebras. International Journal of Theoretical Physics, 2005, 44(7): 793–806
[16] Avallone A, Barbieri G, Vitolo P. Hahn decomposition of modular measures and applications. Annales Societatis Mathematicae Polonae, Ser. I: Commentationes Mathematicae, 2003, 43(2): 149–168
/
| 〈 |
|
〉 |