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Abstract

In $[3] $, J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset $E$ of ${\mathbb R}^{n}$, in the case of intersections of non-quasi-analytic classes with moderate growth and a /Lojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every $C^{\infty }$-Whitney jet belongs to one of them. We also prove a linear extension theorem in the case of a compact set with Markov's property. These extensions of jets can be chosen to be real-analytic on ${\mathbb R}^{n}\setminus E$. Then we prove a /Lojasiewicz theorem.