TY - JOUR

T1 - An application of ergodic theory to a problem in geometric Ramsey theory

AU - Ziegler, Tamar

PY - 1999

Y1 - 1999

N2 - Let E be a measurable subset of ℝk, k > 2, with D̄(E) > 0. Let V = {0, v1,..., vk+1} ∈ ℝk, where v1,..., vk+1 are affinely independent. We show that for r large enough, we can find an isometric copy of rV arbitrarily close to E. This is a generalization of a theorem of Furstenberg, Katznelson and Weiss [FKW] showing a similar property for ℝ2, V = {0, v1, v2}.

AB - Let E be a measurable subset of ℝk, k > 2, with D̄(E) > 0. Let V = {0, v1,..., vk+1} ∈ ℝk, where v1,..., vk+1 are affinely independent. We show that for r large enough, we can find an isometric copy of rV arbitrarily close to E. This is a generalization of a theorem of Furstenberg, Katznelson and Weiss [FKW] showing a similar property for ℝ2, V = {0, v1, v2}.

UR - http://www.scopus.com/inward/record.url?scp=0039446470&partnerID=8YFLogxK

U2 - 10.1007/BF02785583

DO - 10.1007/BF02785583

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AN - SCOPUS:0039446470

SN - 0021-2172

VL - 114

SP - 271

EP - 288

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -