LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES

doi:10.1016/S0252-9602(13)60028-4

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (3): 653-677.doi: 10.1016/S0252-9602(13)60028-4

LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES

Anna AVALLONE|Paolo VITOLO

Dipartimento di Matematica e Informatica, Universit`a della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy

收稿日期:2011-11-17 出版日期:2013-05-20 发布日期:2013-05-20

LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES

Anna AVALLONE|Paolo VITOLO

Dipartimento di Matematica e Informatica, Universit`a della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy

Received:2011-11-17 Online:2013-05-20 Published:2013-05-20

摘要/Abstract

摘要：

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.

关键词: Pseudo-effect algebra, pseudo-D-lattice, D-uniformity, lattice uniformity, mod-ular measure

Abstract:

Key words: Pseudo-effect algebra, pseudo-D-lattice, D-uniformity, lattice uniformity, mod-ular measure

中图分类号:

28B10

Anna AVALLONE, Paolo VITOLO. LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES[J]. 数学物理学报(英文版), 2013, 33(3): 653-677.

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.

参考文献

[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

LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES

LEBESGUE DECOMPOSITION AND BARTLE–DUNFORD–SCHWARTZ THEOREM IN PSEUDO-D-LATTICES

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