Israel Journal of Mathematics

, Volume 114, Issue 1, pp 271–288 | Cite as

An application of ergodic theory to a problem in geometric ramsey theory

  • Tamar Ziegler


LetE be a measurable subset of ℝ k ,k>2, with XXX(E)>0. LetV = {0,υ 1, …,υ k+1} ε ℝ k , whereυ 1, …,υ k+1 are affinely independent. We show that forr large enough, we can find an isometric copy ofrV arbitrarily close toE. This is a generalization of a theorem of Furstenberg, Katznelson and Weiss [FKW] showing a similar property for ℝ2,V = {0,υ 1,υ 2}.


Ergodic Theory Haar Measure Ergodic Theorem Measurable Subset Compact Abelian Group 
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Copyright information

© Hebrew University 1999

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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