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
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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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