  It is shown that the limits of the nested subclasses of five classes of
infinitely divisible distributions on $R^d$, which are the Jurek class, the
Goldie-Steutel-Bondesson class, the class of selfdecomposable distributions,
the Thorin class and the class of generalized type $G$ distributions, are
identical with the closure of the class of stable distributions. More general
results are also given.
