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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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