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Une caracterisation du type de la loi de Cauchy-conforme sur ℝn
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  • Published: March 1988

Une caracterisation du type de la loi de Cauchy-conforme sur ℝn

  • Jean-Louis Dunau1 nAff2 &
  • Henri Sénateur1 

Probability Theory and Related Fields volume 77, pages 129–135 (1988)Cite this article

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  • 3 Citations

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Résumé

La loi de Cauchy-conforme est la mesure de probabilité sur ℝn de densitéC/(1+‖X‖2)n. Le type d'une mesure μ sur ℝn étant l'ensemble des mesures images de μ par les similitudes-translations de ℝn et μ étant une mesure de probabilité sans atome, on démontre que le type de μ est invariant par les inversions de ℝn si et seulement si μ est du type de la loi de Cauchy-conforme.

Abstract

The conformal Cauchy law is the probability on ℝn with densityC/(1+‖X‖2)n. It is shown that for a non-atomic measure μ on ℝn the following is true: its type is invariant under inversions of ℝn if and only if it is the type of a conformal Cauchy law. (The type of a measure is defined as the set of its images under similarities and translations.)

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Références

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  4. Dunau, J.L., Sénateur, H.: Une caractérisation du type de la loi de Cauchy-Heisenberg. (Lect. Notes Math., vol. 1210, pp. 41–57) Berlin Heidelberg New York: Springer 1986

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  7. Letac, G.: Seul le groupe des similitudes-inversions préserve le type de la loi de Cauchy-conforme de ℝn pourn>1. J. Funct. Anal.68, 43–54 (1986)

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Author notes
  1. Jean-Louis Dunau

    Present address: INSA Toulouse, Toulouse, France

Authors and Affiliations

  1. Laboratoire de Statistique et Probabilités, U.A. CNRS 745, Université Paul Sabatier, F-31062, Toulouse Cedex, France

    Jean-Louis Dunau & Henri Sénateur

Authors
  1. Jean-Louis Dunau
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  2. Henri Sénateur
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Dunau, JL., Sénateur, H. Une caracterisation du type de la loi de Cauchy-conforme sur ℝn . Probab. Th. Rel. Fields 77, 129–135 (1988). https://doi.org/10.1007/BF01848135

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  • Received: 02 April 1986

  • Issue Date: March 1988

  • DOI: https://doi.org/10.1007/BF01848135

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