Abstract: An random vector is -substable, if for
some symmetric -stable random vector a random variable with the Laplace
transform and are independent. We say that an random vector
is maximal if it is not -substable for any

In the paper we show that the canonical spectral measure for every -substable
random vector is equivalent to the Lebesgue measure on We show also
that every such vector admits the representation where is an
sub-Gaussian random vector, is a maximal random vector, and are
independent. The last representation is not unique.