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Atomic Intersection of s-Fields and Some of Its Consequences


  • Patrizia Berti

    (Università di Modena e Reggio Emilia)

  • Luca Pratelli

    (Accademia Navale di Livorno)

  • Pietro Rigo

    (Department of Economics and Quantitative Methods, University of Pavia)


Let (omega,F,P) be a probability space. For each G in F, define G as the s-field generated by G and those sets f in F satisfying P(f) in {0, 1}. Conditions for P to be atomic on the intersection of the complements of Ai for i=1,..,k, with A1, . . . ,Ak in F sub-s-fields, are given. Conditions for P to be 0-1-valued on the intersection of the complements of Ai for i=1,..,k are given as well. These conditions are useful in various fields, including Gibbs sampling, iterated conditional expectations and the intersection property.

Suggested Citation

  • Patrizia Berti & Luca Pratelli & Pietro Rigo, 2009. "Atomic Intersection of s-Fields and Some of Its Consequences," Quaderni di Dipartimento 096, University of Pavia, Department of Economics and Quantitative Methods.
  • Handle: RePEc:pav:wpaper:096

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    References listed on IDEAS

    1. Berti, Patrizia & Pratelli, Luca & Rigo, Pietro, 2006. "Asymptotic behaviour of the empirical process for exchangeable data," Stochastic Processes and their Applications, Elsevier, vol. 116(2), pages 337-344, February.
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