On the support of certain symmetric stable probability measures on 𝑇𝑉𝑆

Rajput, Balram S.

doi:10.1090/S0002-9939-1977-0445594-2

On the support of certain symmetric stable probability measures on $\textrm {TVS}$
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Proc. Amer. Math. Soc. 63 (1977), 306-312 Request permission

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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Probability theory

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