Counterexamples in Algebraic Probability Theory

  • András Zempléni


The aim of this paper is to present some results concerning algebraic probability theory introduced by I.Z.Ruzsa and G.J.Székely [5] which show that some of the results in [5] and [8] cannot be generalized without any further assumptions.


Convolution Lution 


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  1. [1]
    A. A. Balkema and S. I. Resnick, Maxinfinite divisibility, J. Appl. Prob. 14 309–319 (1977).MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    F. S. Cater, Choice sets and measurable sets, Rocky Mountain J. Math. 11 499–500 (1981).MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    L. de Haan, A spectral decomposition for max-stable processes, Ann. Prob. 12 1194–1204 (1984).MATHCrossRefGoogle Scholar
  4. [4]
    P. Ressel, Some continuity and measurability results on spaces of measures, Math. Scand. 40 69–78 (1977).MathSciNetMATHGoogle Scholar
  5. [5]
    I. Z. Ruzsa and G. J. Székely, “Algebraic Probability Theory,” Wiley, New York (1988).MATHGoogle Scholar
  6. [6]
    P. Vataan, Max-infinite divisibility and max-stability in infinite dimensions, in: “Probability in Ba-nach Spaces V.,” 400–425, Lecture Notes in Math., Springer, Berlin (1985).CrossRefGoogle Scholar
  7. [7]
    A. Zempléni, The description of the class Jo in the multiplicative structure of distribution functions, in: “Proc. of the 6th Pannonian Symp. on Mathematical Statistics,” 291–305. Reidel Publ. Co., Dordrecht (1987).Google Scholar
  8. [8]
    A. Zempléni, The heredity of Hun and Hungarian Property, J. Theor. Prob. 3 599–609 (1990).MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • András Zempléni
    • 1
  1. 1.Department of Probability Theory and StatisticsEötvös Loránd UniversityBudapestHungary

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