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Israel Journal of Mathematics

, Volume 55, Issue 2, pp 147–152 | Cite as

On hilbertian subsets of finite metric spaces

  • J. Bourgain
  • T. Figiel
  • V. Milman
Article

Abstract

The following result is proved: For everyε>0 there is aC(ε)>0 such that every finite metric space (X, d) contains a subsetY such that |Y|≧C(ε)log|X| and (Y, d Y) embeds (1 +ε)-isomorphically into the Hilbert spacel 2.

Keywords

Hilbert Space Equivalence Relation Convex Body Euclidean Plane Absolute Constant 
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.

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References

  1. 1.
    A. Dvoretzky,Some results on convex bodies and Banach spaces, Proc. Int. Symp. on Linear Spaces, Jerusalem, 1961, pp. 123–160.Google Scholar

Copyright information

© Hebrew University 1986

Authors and Affiliations

  • J. Bourgain
    • 1
  • T. Figiel
    • 2
  • V. Milman
    • 3
  1. 1.University of Illinois and IHESUSA
  2. 2.Polish Academy of SciencesPoland
  3. 3.Tel Aviv UniversityIsrael

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