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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the support of certain symmetric stable probability measures on $ {\rm TVS}$


Author: Balram S. Rajput
Journal: Proc. Amer. Math. Soc. 63 (1977), 306-312
MSC: Primary 60G15; Secondary 60B05
MathSciNet review: 0445594
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Abstract: Let E be a LCTVS, and let $ \mu $ be a $ \tau $-regular symmetric stable probability measure of type $ \alpha \in [1,2]$ on E. Then, it is shown that the topological support $ {S_\mu }$ of $ \mu $ is a (closed) subspace of E. Further, if $ \mu $ satisfies an additional regularity condition, then it is shown that $ {S_\mu }$ is the E-closure of a Banach space contained in E. Specializing these results for $ \alpha = 2$, simple proofs of all the known results regarding the support of centered Gaussian probability measures on LCTV spaces are obtained as corollaries.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0445594-2
PII: S 0002-9939(1977)0445594-2
Keywords: Stable probability measure, topological support, topological vector space, Gaussian probability measure
Article copyright: © Copyright 1977 American Mathematical Society