The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

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It is shown that the limits of the nested subclasses of five classes of infinitely divisible distributions on Rᵈ, 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.