Central Elements in Pseudo-D-Lattices and Hahn Decomposition Theorem
Avallone, Anna ; Barbieri, Giuseppina ; Vitolo, Paolo
Bollettino dell'Unione Matematica Italiana, Tome 3 (2010), p. 447-470 / Harvested from Biblioteca Digitale Italiana di Matematica
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We prove a Hahn decomposition theorem for modular measures on pseudo-D-lattices. As a consequence, we obtain a Uhl type theorem and a Kadets type theorem concerning compactness and convexity of the closure of the range.

Publié le : 2010-10-01
@article{BUMI_2010_9_3_3_447_0,
     author = {Anna Avallone and Giuseppina Barbieri and Paolo Vitolo},
     title = {Central Elements in Pseudo-D-Lattices and Hahn Decomposition Theorem},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {3},
     year = {2010},
     pages = {447-470},
     zbl = {1229.03053},
     mrnumber = {2742776},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2010_9_3_3_447_0}
}

Avallone, Anna; Barbieri, Giuseppina; Vitolo, Paolo. Central Elements in Pseudo-D-Lattices and Hahn Decomposition Theorem. Bollettino dell'Unione Matematica Italiana, Tome 3 (2010) pp. 447-470. http://gdmltest.u-ga.fr/item/BUMI_2010_9_3_3_447_0/

[1] Avallone, A. - Barbieri, G., Range of finitely additive fuzzy measures, Fuzzy Sets and Systems, 89 (2) (1997), 231-241. | MR 1456048 | Zbl 0918.28020

[2] Avallone, A. - Barbieri, G., Lyapunov measures on effect algebras, Comment. Math. Univ. Carolin., 44 (2003), 389-397. | MR 2025808 | Zbl 1097.22002

[3] Avallone, A. - Vitolo, P., Pseudo-D-lattices and topologies generated by measures, Ital. J. Pure Appl. Math., To appear. | MR 3009591 | Zbl 1329.28023

[4] Avallone, A. - Barbieri, G. - Vitolo, P., Hahn decomposition of modular measures and applications, Comment. Math. Prace Mat., 43 (2003), 149-168. | MR 2029889 | Zbl 1043.28009

[5] Barbieri, G., Lyapunov's theorem for measures on D-posets, Internat. J. Theoret. Phys., 43 (2004), 1613-1623. | MR 2108298 | Zbl 1081.81007

[6] Bennett, M. K. - Foulis, D. J., Effect algebras and unsharp quantum logics. Special issue dedicated to Constantin Piron on the occasion of his sixtieth birthday, Found. Phys., 24 (10) (1994), 1331-1352. | MR 1304942

[7] Butnariu, D. - Klement, P., Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer Academic Publishers, Dordrecht, 1993. | MR 2867321 | Zbl 0804.90145

[8] Chovanek, F. - Kopka, F., D-posets, Math. Slovaca, 44 (1) (1994), 21-34. | MR 1290269

[9] Dvurečenskij, A., Central elements and Cantor-Bernstein theorem for pseudo-effect algebras, Journal of the Australian Mathematical Society, 74 (2003), 121-143. | MR 1948263

[10] Dvurečenskij, A. - PULMANNOVÁ, New trends in quantum structures, Kluwer Academic Publishers, Dordrecht; Ister Science, Bratislava, 2000. | MR 1861369

[11] Dvurečenskij, A. - Vetterlein, T., Congruences and states on pseudoeffect algebras, Found. Phys. Letters, 14 (2001), 425-446. | MR 1857794

[12] Epstein, L. G. - Zhang, J., Subjective probabilities on subjectively unambiguous events, Econometrica, 69 (2) (2001), 265-306. | MR 1819756 | Zbl 1020.91048

[13] Georgescu, G. - Iorgulescu, A., Pseudo-BCK algebras: an extension of BCK algebras, Combinatorics, computability and logic (2001), 97-114. | MR 1934824 | Zbl 0986.06018

[14] Pulmannová, S., Generalized Sasaki projections and Riesz ideals in pseudoeffect algebras, International Journal of Theoretical Physics, 42 (7) (2003), 1413-1423. | MR 2021220 | Zbl 1053.81008

[15] Kadets, V. M., A remark on Lyapunov's theorem on a vector measure, Funct. Anal. Appl., 25 (4) (1991), 295-297. | MR 1167727 | Zbl 0762.46031

[16] Yun, S. - Yongming, L. - Maoyin, C., Pseudo difference posets and pseudo Boolean D-posets, Internat. J. Theoret. Phys., 43 (12) (2004), 2447-2460. | MR 2110077 | Zbl 1059.81018

[17] Uhl, J., The range of a vector-valued measure, Proc. Amer. Math. Soc., 23 (1969), 158-163. | MR 264029 | Zbl 0182.46903

[18] Weber, H., Uniform lattices. I. A generalization of topological Riesz spaces and topological Boolean rings, Ann. Mat. Pura Appl., 160 (4) (1991), 347-370. | MR 1163215 | Zbl 0790.06006

[19] Weber, H., On modular functions, Funct. Approx. Comment. Math., 24 (1996), 35-52. | MR 1453447 | Zbl 0887.06011

[20] Weber, H., Uniform lattices and modular functions, Atti Sem. Mat. Fis. Univ. Modena, 47 (1) (1999), 159-182. | MR 1694416 | Zbl 0989.28007