Electronic Communications in Probability

Uniform Upper Bound for a Stable Measure of a Small Ball

Michal Ryznar and Tomasz Zak

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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 $\alpha$.

Article information

Electron. Commun. Probab., Volume 3 (1998), paper no. 9, 75-78.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60B11: Probability theory on linear topological spaces [See also 28C20]
Secondary: 69E07

stable measure small ball

This work is licensed under aCreative Commons Attribution 3.0 License.


Ryznar, Michal; Zak, Tomasz. Uniform Upper Bound for a Stable Measure of a Small Ball. Electron. Commun. Probab. 3 (1998), paper no. 9, 75--78. doi:10.1214/ECP.v3-995. https://projecteuclid.org/euclid.ecp/1456935915

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