... and we want to show that this limit is also equal to the closure of the class of the stable distributions For the proof, we need our new mapping Namely, the proof is based on the fact that (µ) ... Goldie- Steutel- Bondesson class of infinitely divisible distributions on d by Υ-mapping ALEA Lat Am J Probab Math Stat 3, 55–66 (2007) MR2324748 [8] Maejima, M and Nakahara, G.: A note on new classes of infinitely divisible ... 0, and furthermore to the two-sided case The second motivation is the following In Maejima and Sato [9], they showed that the limits of nested subclasses constructed by iterations of several mappings...