Effect algebras and extensions of measures
Avallone, Anna ; De Simone, Anna ; Vitolo, Paolo
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 423-444 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

We investigate the existence of a Caratheodory type extension for modular measures defined on lattice-ordered effect algebras.

Si affronta il problema dell'esistenza di un'estensione tipo Caratheodory per misure modulari definite su lattice-ordered effect algebras.

Publié le : 2006-06-01
@article{BUMI_2006_8_9B_2_423_0,
     author = {Anna Avallone and Anna De Simone and Paolo Vitolo},
     title = {Effect algebras and extensions of measures},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {423-444},
     zbl = {1115.28010},
     mrnumber = {2233145},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_2_423_0}
}

Avallone, Anna; De Simone, Anna; Vitolo, Paolo. Effect algebras and extensions of measures. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 423-444. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_2_423_0/

[1] Alfsen, E.M., Order theoretical foundations of integration, Math. Ann.149, 419-461 (1963). | Zbl 0111.25605

[2] Avallone, A., Lattice uniformities on orthomodular structures, Math. Slovaca51, n. 4, 403-419 (2001). | Zbl 1015.28014

[3] Avallone, A. - Basile, A., On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286, 378-390 (2003). | Zbl 1052.28011

[4] Avallone, A. - De Simone, A., Extension of modular functions on orthomodular lattices, Ital. J. Pure Appl. Math. 9, 109-122 (2001). | Zbl 1008.28011

[5] Avallone, A. - Vitolo, P., Decomposition and control theorems in effect algebras, Sci. Math. Jpn. 58, n.1, 1-14 (2003). | Zbl 1043.03046

[6] Avallone, A. - Vitolo, P., Lattice uniformities on effect algebras, Internat. J. Theoret. Phys. 44, n. 7 (2005), 793-806. | Zbl 1104.81008

[7] Avallone, A. - Barbieri, G. - Vitolo, P., Hahn decomposition of modular measures and applications, Annales Soc. Math. Polon. Series I: Comment. Math. 43, n. 2 (2003), 149-168. | Zbl 1043.28009

[8] Barbieri, G., Liapunov's theorem for measures on D-posets, Internat. J. Theoret. Phys.43, n. 7-8 (2004), 1613-1623.

[9] Barbieri, G. - Weber, H., A topological approach to the study of fuzzy measures, Functional Analysis and Economic Theory, 17-46, Springer (1998). | Zbl 0916.28015

[10] Beltrametti, E.G. - Cassinelli, G., The logic of Quantum Mechanics, Addison Wesley Publishing Co., Reading, Mass (1981). | Zbl 0491.03023

[11] Bennett, M.K. - Foulis, D.J., Effect algebras and unsharp quantum logics, Found. Phys. 24, n.10, 1331-1352 (1994). | Zbl 1213.06004

[12] Butnariu, D. - Klement, P., Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Kluwer Acad. Publ. (1993). | Zbl 0804.90145

[13] D'Andrea, A.B. - De Lucia, P. - Wright, J.D.M., On Kalmbach measurability, Appl. Math. 39, n.6, 445-447 (1994).

[14] Diestel, J. - Uhl, J.J., Vector Measures, Amer. Math. Soc. (1977).

[15] Drewnowski, L., Topological ring of sets, Continuous set functions, Integration, Bull. Acad. Polon. Sci. ser. Sci. Math. Astronom. Phys.20, 269-276 (1972). | Zbl 0249.28004

[16] Dvurečenskij, A. - Pulmannová, S., New Trends in Quantum Structures, Kluwer Acad. Publ. (2000).

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

[18] Fleischer, I. - Traynor, T., Equivalence of group-valued measure on an abstract lattice, Bull. Acad. Pol. Sci., Ser. Sci Math. 28, 549-556 (1980). | Zbl 0514.28004

[19] Ghirardato, P. - Marinacci, M., Ambiguity made precise: a comparative foundation, J. Econom. Theory 102, 251-289 (2002). | Zbl 1019.91015

[20] Hamhalter, J. - Navara, M. - Pták, P., States on orthoalgebras, Internat. J. Theoret. Phys. 34, n.8, 1439-1465 (1995). | Zbl 0841.03034

[21] Herer, W., On the extension of measures with values in a topological group, Annal. Soc. Math. Polon. Series I: Comment. Math.19, 73-80 (1976). | Zbl 0354.28008

[22] Jenča, G., Blocks of homogeneous effect algebras, Bull. Austral. Math. Soc.64, n.1, 81-98 (2001). | Zbl 0985.03063

[23] Pap, E., Null-Additive Set Functions, Mathematics and its Applications, 337, Kluwer Academic Publishers Group, Dordrecht; Ister Science, Bratislava (1995). | Zbl 0968.28010

[24] Riečan, B., The measure extension theorem for subadditive probability measures in orthomodular σ-continuous lattices, Comm. Math. Univ. Carolin.202, 309-315 (1979).

[25] Rǔttimann, G.T. - Wright, J.D.M., Kalmbach outer measures and valuations, Arch. Math. 64, n.6, 523-529 (1995). | Zbl 0820.28002

[26] Weber, H., Fortsetzung von Massen mit Werten in uniformen Halbgruppen, Arch. Math.27, 412-423 (1976). | Zbl 0331.28005

[27] Weber, H., Uniform Lattices I; Uniform lattices II, Ann. Mat. Pura Appl.160, 347-370 (1991) and 165, 133-158 (1993). | Zbl 0790.06006

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

[29] Weber, H., Uniform lattices and modular functions, Atti Sem. Mat. Fis. Univ. Modena47, 159-182 (1999). | Zbl 0989.28007

[30] Zhang, J., Qualitative probabilities and λ-systems, Math. Social Sci.38, 11-20 (1999). | Zbl 0944.91010