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International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems

IPMU 2012: Advances in Computational Intelligence pp 226–234Cite as

State-Complete Riesz MV-Algebras and L-Measure Spaces

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Part of the Communications in Computer and Information Science book series (CCIS,volume 298)

Abstract

State-complete Riesz MV-algebras are a particular class of probability MV-algebras. We associate to any state-complete Riesz MV-algebra (A,s) a measure space (X,Ω,μ) such that (A,s) and (L 1(μ) u ,s μ ) are isometrically isomorphic Riesz MV-algebras, where L 1(μ) u is an interval of L 1(μ) and s μ is the integral. This result can be seen as an analogue of Kakutani’s concrete representation for L-spaces [10] and it leads to a categorical duality between Riesz MV-algebras and a special class of measure spaces (called L-measure spaces).

Keywords

  • Riesz MV-algebra
  • state
  • L-space
  • L-measure space

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, C.P. 010014, Bucharest, Romania

    Ioana Leuştean

Authors
  1. Ioana Leuştean
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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Leuştean, I. (2012). State-Complete Riesz MV-Algebras and L-Measure Spaces. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_25

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  • DOI: https://doi.org/10.1007/978-3-642-31715-6_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

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