Nilfactors of ℝm - Actions and configurations in sets of positive upper density in ℝm

Tamar Ziegler*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We use ergodic theoretic tools to solve a classical problem in geometric Ramsey theory. Let E be a measurable subset of ℝm, with D̄(E) > 0. Let V = {0, v1,..., vk} ⊆ ℝm. We show that for t large enough, we can find an isometric copy of tV arbitrarily close to E. This is a generalization of a theorem of Furstenberg, Katznelson and Weiss [FuKaW] showing a similar property for m = k = 2.

Original languageAmerican English
Pages (from-to)249-266
Number of pages18
JournalJournal d'Analyse Mathematique
Volume99
DOIs
StatePublished - 2006
Externally publishedYes

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