Avallone, De Simone, Vitolo: Effect algebras and extensions of measures

Avallone, Anna and De Simone, Anna and Vitolo, Paolo:
Effect algebras and extensions of measures
Bollettino dell'Unione Matematica Italiana Serie 8 9-B (2006), fasc. n.2, p. 423-444, (English)
pdf (417 Kb), djvu (209 Kb). | MR 2233145 | Zbl 1115.28010

Sunto

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

Referenze Bibliografiche

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

[2] A. AVALLONE, Lattice uniformities on orthomodular structures, Math. Slovaca 51, n. 4, 403-419 (2001). | fulltext EuDML | Zbl 1015.28014

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

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

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

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

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

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

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

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

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

[13] A.B. D'ANDREA - P. DE LUCIA - J.D.M. WRIGHT, On Kalmbach measurability, Appl. Math. 39, n.6, 445-447 (1994). | fulltext EuDML

[14] J. DIESTEL - J.J. UHL, Vector Measures, Amer. Math. Soc. (1977).

[15] L. DREWNOWSKI, 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] A. DVUREČENSKIJ - S. PULMANNOVÁ, New Trends in Quantum Structures, Kluwer Acad. Publ. (2000).

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

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

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

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

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

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

[24] B. RIEČAN, The measure extension theorem for subadditive probability measures in orthomodular $\sigma$-continuous lattices, Comm. Math. Univ. Carolin. 202, 309-315 (1979). | fulltext EuDML

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

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

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

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

[29] H. WEBER, Uniform lattices and modular functions, Atti Sem. Mat. Fis. Univ. Modena 47, 159-182 (1999). | Zbl 0989.28007

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

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche