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The uniform concentration of measure phenomenon in ℓ n p (1 ≤ p ≤ 2)

Part of the Lecture Notes in Mathematics book series (LNM,volume 1745)

Abstract

We prove the uniform concentration of Lebesgue measure phenomenon on the ball of ℓ n p for 1 ≤ p ≤ 2. In particular, we give a first concentration inequality for Lebesgue measure on the ball of ℓ n1 . An application is the lower exponential bound on the dimension of ℓ admitting an isomorphic embedding of ℓ n1 and on the distortion of such those embeddings, proved in [L].

Keywords

  • Lebesgue Measure
  • Unit Ball
  • Convex Body
  • Isoperimetric Inequality
  • Borel Subset

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported by DGICYT grant #PB96-1327. This paper includes part of the Ph.D. thesis of the second author.

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© 2000 Springer-Verlag

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Arias-de-Reyna, J., Villa, R. (2000). The uniform concentration of measure phenomenon in ℓ n p (1 ≤ p ≤ 2). In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107203

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  • DOI: https://doi.org/10.1007/BFb0107203

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41070-6

  • Online ISBN: 978-3-540-45392-5

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