Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

6 Issues per year


IMPACT FACTOR 2016: 0.346
5-year IMPACT FACTOR: 0.412

CiteScore 2016: 0.42

SCImago Journal Rank (SJR) 2016: 0.489
Source Normalized Impact per Paper (SNIP) 2016: 0.745

Mathematical Citation Quotient (MCQ) 2016: 0.24

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 67, Issue 4

Issues

Outer measure on effect algebras

Akhilesh Kumar Singh
  • Corresponding author
  • Department of Mathematics Jaypee Institute of Information Technology (Deemed University) Noida-201 304, Uttar Pradesh India
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2017-07-14 | DOI: https://doi.org/10.1515/ms-2017-0012

Abstract

In the present paper, the notion of an outer measure m* on lattice ordered effect algebras L is introduced and investigated. Carathéodory’s criterion for the outer measure m* is given and established on L. Properties of an induced outer measure m* defined on a lattice ordered effect algebra L are studied and finally, Choquet theorem is proved for the induced outer measure m* on a σ-complete lattice ordered effect algebra L.

MSC 2010: Primary 06A11; 28A12; 28E99; 06C15

Keywords: outer measure; Carathéodory’s theorem; Choquet lemma; effect algebras

References

  • [1]

    Avallone, A.—Basile, A.: On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2003), 378–390.Google Scholar

  • [2]

    Avallone, A.—De Simone, A.—Vitolo, P.: Effect algebras and extensions of measures, Bullenttino U.M.I. 9-B(8) (2006), 423–444.Google Scholar

  • [3]

    Bennet, M. K.—Foulis, D. J.: Effect algebras and unsharp quantum logics, Found. Phys. 24(10) (1994), 1331–1352.Google Scholar

  • [4]

    Bennet, M. K.—Foulis, D. J.: Phi-symmetric effect algebras, Found. Phys. 25 (1995), 1699–1722.Google Scholar

  • [5]

    Bennet, M. K.—Foulis, D. J.—Greechie, R. J.: Sums and products of interval algebras, Inter. J. Theoret. Phys. 33 (1994), 2114–2136.Google Scholar

  • [6]

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

  • [7]

    Butnariu, D.—Klement, E. P.: Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer Acad. Pub., 1993.Google Scholar

  • [8]

    Busch, P.—Lahiti, P. J.—Mittelstaedt, P.: The Quantum Theory of Measurement. Lecture Notes in Physics, Springer-Verlag, Berlin, 1991.Google Scholar

  • [9]

    Chang, C.: Algebraic analysis of many valued logic, Trans. Amer. Math. Soc., 89 (1959), 74–80.Google Scholar

  • [10]

    Dvurečenskij, A.—Pulmannova´, S.: New Trends in Quantum Structures, Kluwer Acad. Pub., 2000.Google Scholar

  • [11]

    Dvurečenskij, A.: The lattice and simplex structure of states on pseudo effect algebras, Inter. J. Theoret Phys. 50 (2011), 2758–2775.Google Scholar

  • [12]

    Epstein, L. G.—Zhang, J.: Subjective probabilities on subjectively unambiguous events, Econometrica 69(2) (2001), 265–306.CrossrefGoogle Scholar

  • [13]

    Guintini, R.—Greuling, R.: Towards a formal language for unsharp properties, Found. Phys. 19 (1989), 931–945.Google Scholar

  • [14]

    Kôpka, F.—Chovanec, F.: D-posets of fuzzy sets, Tatra Mt. Math. Publ. 1 (1992), 83–87.Google Scholar

  • [15]

    Khare, M.—Singh, A. K.: Atom and a Saks type decomposition in effect algebras, Demonstratio Math. 38(1) (2008), 59–70.Google Scholar

  • [16]

    Khare, M.—Singh, A. K.: Atoms and Dobrakov submeasures in effect algebras, Fuzzy Sets and Systems 159 (2008), 1123–1128.Google Scholar

  • [17]

    Khare, M.—Singh, A. K.: Weakly tight functions, their Jordan type decomposition and total variation in effect algebras, J. Math. Anal. Appl. 344(1) (2008), 535–545.Web of ScienceGoogle Scholar

  • [18]

    Khare, M.—Singh, A. K.: Pseudo-atoms, atoms and a Jordan type decomposition in effect algebras, J. Math. Anal. Appl. 344(1) (2008), 238–252.Web of ScienceGoogle Scholar

  • [19]

    Michalikova´, A.: Outer measure on MV-algebras. In: New Dimensions in Fuzzy Logic and Related Technologies, 2007, pp. 237–240.Google Scholar

  • [20]

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

  • [21]

    Pap, E.: Handbook of Measure Theory, Elsevier, North-Holland, 2002.Google Scholar

  • [22]

    Rudin, W.: Real and Complex Analysis, Mc Graw-Hill, 1966.Web of ScienceGoogle Scholar

About the article


Received: 2015-05-30

Accepted: 2015-09-03

Published Online: 2017-07-14

Published in Print: 2017-08-28


Citation Information: Mathematica Slovaca, Volume 67, Issue 4, Pages 811–818, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0012.

Export Citation

© 2017 Mathematical Institute Slovak Academy of Sciences. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in