In the theory of the
decomposition of probability laws, the fundamental problem stated by D. A. Raikov
of the characterization of the class I0 of the infinitely divisible laws without
indecomposable factors has been studied in the case of univariate laws by Yu. V.
Linnik and I. V. Ostrovskiy. Lately, we have shown that nearly all these results can
be extended to the case of multivariate laws. In this paper, we give a result which can
be considered as an extension of a theorem of Raikov and P. Lévy and of a
particular case of theorems of Linnik, and the extension of this result to the case of
several variables.
