Abstract
LetE be a locally convex space. Let μ be an absolutely convexly tight Radom semi-stable probability measure onE with index 1≤α<2 and Levy measureM. The main result of this paper shows that the closed semigroup generated by the support ofM and the negative of the barycenter ofM restricted to a suitable compact subset ofE is a (closed) linear space ofE, and that the support of μ is a suitable translate of this linear space. This result complements a few known results concerning the supports of stable and semi-stable probability measures. In particular, it extends an analogous result proved recently for the support of α-stable probability measures 1≤α<2 (Ref. 4). Related results concerning the support of Radon semi-stable probability measures onE of index 0<α<1 are also discussed.
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