Effect algebras and extensions of measures

Anna Avallone; Anna De Simone; Paolo Vitolo

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 423-444
  • ISSN: 0392-4041

Abstract

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

How to cite

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Avallone, Anna, De Simone, Anna, and Vitolo, Paolo. "Effect algebras and extensions of measures." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 423-444. <http://eudml.org/doc/289619>.

@article{Avallone2006,
abstract = {We investigate the existence of a Caratheodory type extension for modular measures defined on lattice-ordered effect algebras.},
author = {Avallone, Anna, De Simone, Anna, Vitolo, Paolo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {423-444},
publisher = {Unione Matematica Italiana},
title = {Effect algebras and extensions of measures},
url = {http://eudml.org/doc/289619},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Avallone, Anna
AU - De Simone, Anna
AU - Vitolo, Paolo
TI - Effect algebras and extensions of measures
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/6//
PB - Unione Matematica Italiana
VL - 9-B
IS - 2
SP - 423
EP - 444
AB - We investigate the existence of a Caratheodory type extension for modular measures defined on lattice-ordered effect algebras.
LA - eng
UR - http://eudml.org/doc/289619
ER -

References

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  1. ALFSEN, E.M., Order theoretical foundations of integration, Math. Ann.149, 419-461 (1963). Zbl0111.25605
  2. AVALLONE, A., Lattice uniformities on orthomodular structures, Math. Slovaca51, n. 4, 403-419 (2001). Zbl1015.28014
  3. AVALLONE, A. - BASILE, A., On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl.286, 378-390 (2003). Zbl1052.28011
  4. AVALLONE, A. - DE SIMONE, A., Extension of modular functions on orthomodular lattices, Ital. J. Pure Appl. Math.9, 109-122 (2001). Zbl1008.28011
  5. AVALLONE, A. - VITOLO, P., Decomposition and control theorems in effect algebras, Sci. Math. Jpn.58, n.1, 1-14 (2003). Zbl1043.03046
  6. AVALLONE, A. - VITOLO, P., Lattice uniformities on effect algebras, Internat. J. Theoret. Phys.44, n. 7 (2005), 793-806. Zbl1104.81008
  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. Zbl1043.28009
  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). Zbl0916.28015
  10. BELTRAMETTI, E.G. - CASSINELLI, G., The logic of Quantum Mechanics, Addison Wesley Publishing Co., Reading, Mass (1981). Zbl0491.03023
  11. BENNETT, M.K. - FOULIS, D.J., Effect algebras and unsharp quantum logics, Found. Phys.24, n.10, 1331-1352 (1994). Zbl1213.06004
  12. BUTNARIU, D. - KLEMENT, P., Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Kluwer Acad. Publ. (1993). Zbl0804.90145
  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). Zbl0249.28004
  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, Econometrica69, n. 2, 265-306 (2001). Zbl1020.91048
  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). Zbl0514.28004
  19. GHIRARDATO, P. - MARINACCI, M., Ambiguity made precise: a comparative foundation, J. Econom. Theory102, 251-289 (2002). Zbl1019.91015
  20. HAMHALTER, J. - NAVARA, M. - PTÁK, P., States on orthoalgebras, Internat. J. Theoret. Phys.34, n.8, 1439-1465 (1995). Zbl0841.03034
  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). Zbl0354.28008
  22. JENČA, G., Blocks of homogeneous effect algebras, Bull. Austral. Math. Soc.64, n.1, 81-98 (2001). Zbl0985.03063
  23. PAP, E., Null-Additive Set Functions, Mathematics and its Applications, 337, Kluwer Academic Publishers Group, Dordrecht; Ister Science, Bratislava (1995). Zbl0968.28010
  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). Zbl0820.28002
  26. WEBER, H., Fortsetzung von Massen mit Werten in uniformen Halbgruppen, Arch. Math.27, 412-423 (1976). Zbl0331.28005
  27. WEBER, H., Uniform Lattices I; Uniform lattices II, Ann. Mat. Pura Appl.160, 347-370 (1991) and 165, 133-158 (1993). Zbl0790.06006
  28. WEBER, H., On modular functions, Funct. Approx. Comment. Math.24, 35-52 (1996). Zbl0887.06011
  29. WEBER, H., Uniform lattices and modular functions, Atti Sem. Mat. Fis. Univ. Modena47, 159-182 (1999). Zbl0989.28007
  30. ZHANG, J., Qualitative probabilities and λ-systems, Math. Social Sci.38, 11-20 (1999). Zbl0944.91010

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