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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the density of the distribution of $ p$-stable seminorms, $ 0<p<1$


Authors: Maciej Lewandowski and Tomasz Żak
Journal: Proc. Amer. Math. Soc. 100 (1987), 345-351
MSC: Primary 60B11; Secondary 60E07
MathSciNet review: 884477
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Abstract: Let $ \mu $ be a symmetric $ p$-stable measure, $ 0 < p < 1$, on a locally convex separable linear metric space $ E$ and let $ q$ be a lower semicontinuous seminorm on $ E$. It is known that $ F(t) = \mu \{ x:q(x) < t\} $ is absolutely continuous with respect to the Lebesgue measure. We prove an explicit formula for the density $ F'(t)$ and give an asymptotic estimate of it at infinity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0884477-7
PII: S 0002-9939(1987)0884477-7
Keywords: Stable measures, seminorms, density
Article copyright: © Copyright 1987 American Mathematical Society