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Seul le groupe des similitudes-inversions préserve le type de la loi de Cauchy-conforme de $${\mathbb{R}}^ n$$ pour $$n>1$$. (Only the group of similitude-inversions preserves the Cauchy-conformal type distributions of $${\mathbb{R}}^ n$$ for $$n>1)$$. (French) Zbl 0612.60019
On $${\mathbb{R}}^ n$$, $$n\geq 2$$ the conformal-Cauchy type distributions are introduced. It is proved that a measurable transform $$F: {\mathbb{R}}^ n\to {\mathbb{R}}^ n$$ preserves this type iff it coincides almost everywhere with either a similitude or an inversion-similitude of $${\mathbb{R}}^ n$$. For the case $$n=1$$ see the author, Proc. Am. Math. Soc. 67(1977), 277-286 (1978; Zbl 0376.28019).
Reviewer: N.Kalinauskaitė

##### MSC:
 6e+100 Distribution theory
##### Keywords:
conformal-Cauchy type distributions
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##### References:
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