Israel Journal of Mathematics

, Volume 52, Issue 1–2, pp 46–52 | Cite as

On lipschitz embedding of finite metric spaces in Hilbert space

  • J. Bourgain


It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn), showing that the positive result is essentially best possible. The methods used are of probabilistic nature. For instance, to construct our example, we make use of random graphs.


Hilbert Space Riemannian Manifold Random Graph Probabilistic Nature Embedding Problem 
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Copyright information

© The Weizmann Science Press of Israel 1985

Authors and Affiliations

  • J. Bourgain
    • 1
  1. 1.Department of MathematicsVrije Universiteit BrusselBrusselsBelgium

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