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


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.


Hilbert Space Equivalence Relation Convex Body Euclidean Plane Absolute Constant 
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  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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