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1998 Uniform Upper Bound for a Stable Measure of a Small Ball
Michal Ryznar, Tomasz Zak
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Electron. Commun. Probab. 3: 75-78 (1998). DOI: 10.1214/ECP.v3-995

Abstract

P. Hitczenko, S.Kwapien, W.N.Li, G.Schechtman, T.Schlumprecht and J.Zinn stated the following conjecture. Let $\mu$ be a symmetric $\alpha$-stable measure on a separable Banach space and $B$ a centered ball such that $\mu(B)\le b$. Then there exists a constant $R(b)$, depending only on $b$, such that $\mu(tB)\le R(b)t\mu(B)$ for all $0 \lt t \lt 1$. We prove that the above inequality holds but the constant $R$ must depend also on $\alpha$.

Citation

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Michal Ryznar. Tomasz Zak. "Uniform Upper Bound for a Stable Measure of a Small Ball." Electron. Commun. Probab. 3 75 - 78, 1998. https://doi.org/10.1214/ECP.v3-995

Information

Accepted: 16 September 1998; Published: 1998
First available in Project Euclid: 2 March 2016

zbMATH: 0907.60009
MathSciNet: MR1645592
Digital Object Identifier: 10.1214/ECP.v3-995

Subjects:
Primary: 60B11
Secondary: 69E07

Keywords: small ball , Stable measure

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