Open Access

Measures: continuity, measurability, duality, extension

   | Nov 12, 2012

[1] ADÁMEK, J.: Theory of Mathematical Structures. Reidel, Dordrecht, 1983.Search in Google Scholar

[2] BUGAJSKI, S.: Statistical maps I. Basic properties, Math. Slovaca 51 (2001), 321-342.Search in Google Scholar

[3] BUGAJSKI, S.: Statistical maps II. Operational random variables, Math. Slovaca 51 (2001), 343-361.Search in Google Scholar

[4] CIGNOLI, R.-D’OTTAVIANO, I. M. L.-MUNDICI, D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publ., Dordrecht, 2000.10.1007/978-94-015-9480-6Search in Google Scholar

[5] DVUREČENSKIJ, A.-PULMANNOV´A, S.: New Trends in Quantum Structures. Math. Appl., Vol. 516, Kluwer Academic Publ., Dordrecht; Ister Science, Bratislava, 2000.10.1007/978-94-017-2422-7Search in Google Scholar

[6] FOULIS, D. J.-BENNETT, M. K.: Effect algebras and unsharp quantum logics, Found. Phys. 24 (1994), 1331-1352.10.1007/BF02283036Search in Google Scholar

[7] FRIČ, R.: Remarks on sequential envelopes, Rend. Istit. Math. Univ. Trieste 20 (1988), 19-28.Search in Google Scholar

[8] FRIČ, R.: A Stone type duality and its applications to probability, Topology Proc. 22 (1999), 125-137.Search in Google Scholar

[9] FRIČ, R.: Boolean algebras: convergence and measure, Topology Appl. 111 (2001), 139-149.10.1016/S0166-8641(99)00195-9Search in Google Scholar

[10] FRIČ, R.: Convergence and duality, Appl. Categ. Structures 10 (2002), 257-266.10.1023/A:1015292329804Search in Google Scholar

[11] FRIČ, R.: _Lukasiewicz tribes are absolutely sequentially closed bold algebras, Czechoslovak Math. J. 52 (2002), 861-874.10.1023/B:CMAJ.0000027239.28381.31Search in Google Scholar

[12] FRIČ, R.: Measures on MV -algebras, Soft Comput. 7 (2002), 130-137.10.1007/s00500-002-0194-6Search in Google Scholar

[13] FRIČ, R.: Duality for generalized events, Math. Slovaca 54 (2004), 49-60.Search in Google Scholar

[14] FRIČ, R.: Coproducts of D-posets and their applications to probability, Internt. J. Theoret. Phys. 43 (2004), 1625-1632.10.1023/B:IJTP.0000048808.83945.08Search in Google Scholar

[15] FRIČ, R.: Remarks on statistical maps and fuzzy (operational) random variables, Tatra Mt. Math. Publ. 30 (2005), 21-34.Search in Google Scholar

[16] FRIČ, R.: Extension of measures: a categorical approach, Math. Bohemica 130 (2005), 397-407.10.21136/MB.2005.134212Search in Google Scholar

[17] FRIČ, R.-JAKUB´IK, J.: Sequential convergences on Boolean algebras defined by systems of maximal filters, Czechoslovak Math. J. 51 (2001) 261-274.Search in Google Scholar

[18] FRIČ, R.-MCKENNON, K.-RICHARDSON, G. D.: Sequential convergence in C(X), in: Proc. Internat. Summer School-Convergence Structures and Applications to Analysis, Frankfurt a.d. Oder, 1978, Abh. Akad. Wiss. DDR, Abt. Math.-Natur.-Technik, Vol. 4, 1979, Akademie-Verlag, Berlin, 1980, pp. 57-65.Search in Google Scholar

[19] GUDDER, S.: Fuzzy probability theory, Demonstratio Math. 31 (1998), 235-254.Search in Google Scholar

[20] JUREČKOV´A, M.: The measure extension theorem for MV -algebras, Tatra Mt. Math. Publ. 6 (1995), 56-61.Search in Google Scholar

[21] KENT, D. C.-RICHARDSON, G. D.: Two generalizations of Nov´ak’s sequential envelope, Math. Nachr. 19 (1979), 77-85.10.1002/mana.19790910106Search in Google Scholar

[22] KÔPKA, F.: D-posets of fuzzy sets, Tatra Mt. Math. Publ. 1 (1992), 95-102.Search in Google Scholar

[23] KÔPKA, F.-CHOVANEC, F.: D-posets, Math. Slovaca 44 (1994), 21-34.Search in Google Scholar

[24] MIŠIK, L., Jr.: Sequential completeness and {0,1}-sequential completeness are different, Czechoslovak Math. J. 34 (1984), 424-431.10.21136/CMJ.1984.101968Search in Google Scholar

[25] NOVÁK, J.: ¨Uber die eindeutigen stetigen Erweiterungen stetiger Funktionen, Czechoslovak Math. J. 8 (1958), 344-355.10.21136/CMJ.1958.100309Search in Google Scholar

[26] NOVÁK, J.: On convergence spaces and their sequential envelopes, Czechoslovak Math. J. 15 (1965), 74-100.10.21136/CMJ.1965.100655Search in Google Scholar

[27] NOVÁK, J.: On sequential envelopes defined by means of certain classes of functions, Czechoslovak Math. J. 18 (1968), 450-456.10.21136/CMJ.1968.100845Search in Google Scholar

[28] PAPČO, M.: On measurable spaces and measurable maps, Tatra Mt. Math. Publ. 28 (2004), 125-140.Search in Google Scholar

[29] PAPČO, M.: On fuzzy random variables: examples and generalizations, Tatra Mt. Math. Publ. 30 (2005), 175-185.Search in Google Scholar

[30] PAPČO, M.: On effect algebras, Soft Comput. 12 (2007), 26-35.10.1007/s00500-007-0171-1Search in Google Scholar

[31] PTÁK, P.-PULMANNOV´A, S.: Orthomodular Structures as Quantum Logics. Fund. Theorie Phys., Vol. 44, Kluwer Acad. Publ., Dordrecht, 1991.Search in Google Scholar

[32] RIEČAN, B.-MUNDICI, D.: Probability on MV -algebras, in: Handbook of Measure Theory, Vol. I, II (E. Pap, ed.), North-Holland, Amsterdam, 2002, pp. 869-909.10.1016/B978-044450263-6/50022-1Search in Google Scholar

[33] RIEČAN, B.-NEUBRUNN, T. Integral, Measure, and Ordering. Math. Appl., Vol. 411, Kluwer Acad. Publ., Dordrecht; Ister Science, Bratislava, 1997.10.1007/978-94-015-8919-2Search in Google Scholar

ISSN:
1210-3195
Language:
English
Publication timeframe:
3 times per year
Journal Subjects:
Mathematics, General Mathematics