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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

60E99 Distribution theory
Full Text: DOI
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