## On the support of symmetric infinitely divisible and stable probability measures on LCTVS

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- by Balram S. Rajput PDF
- Proc. Amer. Math. Soc.
**66**(1977), 331-334 Request permission

## Abstract:

It is shown that the topological support (supp.) of a $\tau$-regular, symmetric, infinitely divisible (resp. stable of any index $\alpha \in (0,2)$) probability measure on a Hausdorff LCTVS*E*is a subgroup (resp. a subspace) of

*E*. The part regarding the support of a stable probability measure of this theorem completes a result of A. De-Acosta [Ann. of Probability

**3**(1975), 865-875], who proved a similar result for $\alpha \in (1,2)$, and the author [Proc. Amer. Math. Soc.

**63**(1977), 306-312], who proved it for $\alpha \in [1,2)$. Further, it provides a complete affirmative solution to the question, raised by J. Kuelbs and V. Mandrekar [Studia Math.

**50**(1974), 149-162], of whether the supp. of a symmetric stable probability measure of index $\alpha \in (0,1]$ on a separable Hilbert space

*H*is a subspace of

*H*.

## References

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—, - I. Csiszár and Balram S. Rajput,
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*On the*$wea{k^\ast }$

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## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**66**(1977), 331-334 - MSC: Primary 60B05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0494351-X
- MathSciNet review: 0494351