On Hilbertian subsets of finite metric spaces
J Bourgain, T Figiel, V Milman - Israel Journal of Mathematics, 1986 - Springer
J Bourgain, T Figiel, V Milman
Israel Journal of Mathematics, 1986•SpringerOn hilbertian subsets of finite metric spaces Page 1 ISRAEL JOURNAL OF MATHEMATICS,
Vol. 55, No, 2, 1986 ON HILBERTIAN SUBSETS OF FINITE METRIC SPACES t BY J.
BOURGAIN," T. FIGIEL h AND V. MILMAN c University o[ Illinois and IHES ; Polish Academy o[
Sciences ; and c Tel A viv University ABSTRACT The following result is proved: For every e >0
there is a C(e)>0 such that every finite metric space (X, d) contains a subset Y such that [ Y [
_-> C(e) log IX[ and (Y, de) embeds (1 + e)-isomorphically into the Hilbert space 12. O …
Vol. 55, No, 2, 1986 ON HILBERTIAN SUBSETS OF FINITE METRIC SPACES t BY J.
BOURGAIN," T. FIGIEL h AND V. MILMAN c University o[ Illinois and IHES ; Polish Academy o[
Sciences ; and c Tel A viv University ABSTRACT The following result is proved: For every e >0
there is a C(e)>0 such that every finite metric space (X, d) contains a subset Y such that [ Y [
_-> C(e) log IX[ and (Y, de) embeds (1 + e)-isomorphically into the Hilbert space 12. O …
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.
Springer