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On hilbertian subsets of finite metric spaces

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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.

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References

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

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Authors and Affiliations

  1. University of Illinois and IHES, USA

    J. Bourgain

  2. Polish Academy of Sciences, Poland

    T. Figiel

  3. Tel Aviv University, Israel

    V. Milman

Authors
  1. J. Bourgain
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  2. T. Figiel
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  3. V. Milman
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Additional information

The authors are grateful to Haim Wolfson for some discussions related to the content of this paper.

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Bourgain, J., Figiel, T. & Milman, V. On hilbertian subsets of finite metric spaces. Israel J. Math. 55, 147–152 (1986). https://doi.org/10.1007/BF02801990

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  • DOI: https://doi.org/10.1007/BF02801990

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