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Aplicacion de las submedidasC a las probabilidades comparativas

  • César R. Ortiz
Article
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Resumen

Introducimos en este trabajo el concepto de submedidaC (comparativa), sobre un álgebra de conjuntosD, estudiamos propiedades de estas submedidas que serán necesarias para la cuantificación de probabilidades comparativas (P. C.) y se relacionan con otro concepto introducido recientemente por Dobrakov, que es el de submedidaI. Se estudian las condiciones bajo las que la convergencia de una sucesión (A n ) enD subordina la convergencia de (A n′ ≥) y la representación cuantitativa de P. C. mediante submedidasC, caracterizándose como subclase aquellas que satisfacen los axiomas de Kolmogorov.

Abstract

In this paper the concept of submeasuresC (comparative) on a fiel of subsetsD is introduced. Some properties of these submeasures in relation to the problem of quantifying comparative probabilities (C. P.) in terms of these submeasures are considered. Also their relationship with Dobrakov's submeasuresI is explored. In particular we study conditions under which convergence of a sequence (A n ) inD subordinates convergence in (A n′ ≥) and quantitative representations of C. P. in terms of submeasuresC (those satisfying Kolmogorov's axioms being a subclase of ours).

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Bibliografia

  1. [1]
    I. DOBRAKOV: “On submeasures I”. Dissertationes Math. (Rozprawy Mat.) 112 (1974).Google Scholar
  2. [2]
    T. FINE: “A note on the existence of Qualitative Probability”. Ann. Math. Statist. 42, 1.182–1.186, (1971).CrossRefMathSciNetGoogle Scholar
  3. [3]
    T. FINE: “Theories of Probability. An examination of Foundations”. Academic Press, 1973.Google Scholar
  4. [4]
    P. C. FISHBURN: “Utility Theory for Decision Marking”. Wiley, 1970.Google Scholar
  5. [5]
    H. J. KOWALSKY: “Topological Spaces”. Academic Press, 1965.Google Scholar
  6. [6]
    C. VILLEGAS: “On Qualitative Probability σ-álgebras”. Ann. Math. Statistic, 35, 1.787–1.796, (1964).MathSciNetGoogle Scholar

Copyright information

© Springer 1981

Authors and Affiliations

  • César R. Ortiz
    • 1
  1. 1.Dto Estadística Matemática Facultad de CienciasUniversidad de MálagaMálagaSpain

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