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Proceedings of the American Mathematical Society

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

 

 

Stable measure of a small ball


Authors: M. Lewandowski, M. Ryznar and T. Żak
Journal: Proc. Amer. Math. Soc. 115 (1992), 489-494
MSC: Primary 60B11
DOI: https://doi.org/10.1090/S0002-9939-1992-1089410-5
MathSciNet review: 1089410
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Abstract: Let $ \mu $ be a symmetric $ p$-stable measure on a Banach space ($ (E,\vert\vert\vert\vert)$. We prove that $ \mu \{ \vert\vert x\vert\vert < t\} \leq Kt$, where the constant $ K$ is independent of all properties of $ \mu $ except for the measure of the unit ball $ \mu \{ \vert\vert x\vert\vert < 1\} $.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1089410-5
Keywords: Stable measure, Gaussian measure, distribution of the norm
Article copyright: © Copyright 1992 American Mathematical Society