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Une caractérisation du type de la loi de Cauchy-conforme sur \({\mathbb{R}}^ n\). (A characterization of the type of the conformal Cauchy law on \({\mathbb{R}}^ n)\). (French) Zbl 0662.62008
Let \(\mu\) be a measure defined on \(R^ n\) and consider the set of the images of \(\mu\) under similarities and translations of \(R^ n\). The authors term this set as the type of \(\mu\) and show that the conformal Cauchy distribution defined by the density \[ f(x)=c/(1+\| x\|^ 2)^ n,\quad x\in R^ n, \] is characterized by the invariance of the type of a non-atomic measure \(\mu\) on \(R^ n\) under inversions of \(R^ n\).
Reviewer: E.Xekalaki

62E10 Characterization and structure theory of statistical distributions
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