Abstract
The exact tail behavior of stable measures in Banach spaces and measures in their domains of attraction is given. Conditions for a p.m. to be in the domain of attraction of a stable p.m. of order α \alpha are derived which are sufficient in type p spaces, p > α p > \alpha , and necessary in general. This paper also contains a short proof of the Lévy-Khinchin formula in Banach spaces.
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