Invariance of nonatomic measures on effect algebras

References

[1] Avallone, A.—Basile, A.: On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2003), 378–390.10.1016/S0022-247X(03)00274-9Search in Google Scholar

[2] Avallone, A.—De Simone, A.—Vitolo, P.: Effect algebras and extensions of measures, Boll. Unione Mat. Ital. 9-B (8) (2006), 423–444.Search in Google Scholar

[3] Bennett, M. K.—Foulis, D. J.: Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1331–1352.10.1007/BF02283036Search in Google Scholar

[4] Bennett, M. K.—Foulis, D. J.: Phi-symmetric effect algebras, Found. Phys. 25 (1995), 1699–1722.10.1007/BF02057883Search in Google Scholar

[5] Bennett, M. K.—Foulis, D. J.—Greechie, R. J.: Sums and products of interval algebras, Internat. J. Theoret. Phys. 33 (1994), 2114–2136.10.1007/BF00675796Search in Google Scholar

[6] Beltrametti, E. G.—Cassinelli, G., The Logic of Quantum Mechanics, Addison-Wesley Publishing Co., Reading, Mass, 1981.Search in Google Scholar

[7] Butnariu, D.—Klement, E. P., Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer Acad. Publ., 1993.10.1007/978-94-017-3602-2Search in Google Scholar

[8] Barbieri G., Liapunov’s theorem for measures on D-posets, Internat. J. Theoret. Phys. 43 (2004), 1613–1623.10.1023/B:IJTP.0000048807.37145.ccSearch in Google Scholar

[9] Dvurečenskij, A.—Pulmannová, S.: New Trends in Quantum Structures, Kluwer Acad. Publ., 2000.10.1007/978-94-017-2422-7Search in Google Scholar

[10] Dvurečenskij, A.—Xie, Y.—Yang, A.: Discrete (n+1)-valued states and n-perfect pseudo effect algebras, Soft Comput. 17 (2013), 1537–1552.10.1007/s00500-013-1001-2Search in Google Scholar

[11] Dinculeanu, N.: Vector Measures, Pergamon Press, Oxford, London, Edinburgh, 1967.10.1016/B978-1-4831-9762-3.50004-4Search in Google Scholar

[12] Epstein L. G.—Zhang, J.: Subjective probabilities on subjectively unambiguous events, Econometrica 69 (2001), 265–306.10.1111/1468-0262.00193Search in Google Scholar

[13] Honda, A.—Okazaki, Y.: Invariance of fuzzy measure, Bull. Kyushu Inst. Tech. Pure Appl. Math. 46 (1999), 1–8.Search in Google Scholar

[14] Jenča, G.: 0-homogenious effect algebras, Soft Comput. 14 (2010), 1111–1116.10.1007/s00500-009-0505-2Search in Google Scholar

[15] Jurečková, M.—Chovanec, F.: On some properties of submeasures on MV-algebras, Math. Slovaca 54 (2004), 161–167.Search in Google Scholar

[16] Klimkin, V. M.—Svistula, M. G.: Darboux property of a non-additive set function, Sb. Math. 192 (2001), 969. 10.1070/5M20010192n07ABEH000578.Search in Google Scholar

[17] Kôpka, F.: D-posets of fuzzy sets, Tatra Mt. Math. Publ. 1 (1992), 83–87.Search in Google Scholar

[18] Khare, M.—Singh, A. K.: Atom and a Saks type decomposition in effect algebras, Novi Sad J. Math. 38 (2008), 59–70.Search in Google Scholar

[19] Khare, M.—Singh, A. K.: Atoms and Dobrakov submeasures in effect algebras, Fuzzy Sets and Systems 159 (2008), 1123–1128.10.1016/j.fss.2007.11.005Search in Google Scholar

[20] Khare, M.—Singh, A. K.: Weakly tight functions, their Jordan type decomposition and total variation in effect algebras, J. Math. Anal. Appl. 344 (2008), 535–545.10.1016/j.jmaa.2008.03.017Search in Google Scholar

[21] Khare, M.—Singh, A. K.: Pseudo-atoms, atoms and a Jordan type decomposition in effect algebras, J. Math. Anal. Appl. 344 (2008), 238–252.10.1016/j.jmaa.2008.03.003Search in Google Scholar

[22] Pap, E.: Null-additive Set Functions. Mathematics and its Applications 337, Kluwer Acad. Press, 1995.Search in Google Scholar

[23] Pap, E.: Handbook of Measure Theory, Elsevier, North-Holland, 2002.Search in Google Scholar

[24] Riečan B.: On the Dobrakov submeasure on fuzzy sets, Fuzzy Sets and Systems 151 (2005), 635–641.10.1016/j.fss.2004.07.004Search in Google Scholar