Central and $L^{p}$-concentration of 1-Lipschitz maps into $\mbi{R}$-trees
Kei FUNANO
Source: J. Math. Soc. Japan Volume 61, Number 2
(2009), 483-506.
Abstract
In this paper, we study the Lévy-Milman concentration phenomenon of 1-Lipschitz maps from mm-spaces to $\mbi{R}$-trees. Our main theorems assert that the concentration to $\mbi{R}$-trees is equivalent to the concentration to the real line.
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53C23
Keywords: median; mm-space; observable $L^{p}$-variation; observable diameter; observable central radius; $\mbi{R}$-tree
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1242220719
Digital Object Identifier: doi:10.2969/jmsj/06120483
Zentralblatt MATH identifier: 05573647
Mathematical Reviews number (MathSciNet): MR2532898
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