WM groups and Ramsey theory

Vitaly Bergelson*, Hillel Furstenberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

For amenable groups there are "correspondence principles" relating the behavior under group translation for sets of positive density to that of sets of positive invariant measure for ergodic actions of the group. When the group is also "minimally almost periodic" such actions are automatically weakly mixing; hence the name WM groups. We study here the combinatorial consequences of this state of affairs.

Original languageEnglish
Pages (from-to)2572-2580
Number of pages9
JournalTopology and its Applications
Volume156
Issue number16
DOIs
StatePublished - 1 Oct 2009

Keywords

  • Amenable
  • Hindman's theorem
  • Minimally almost periodic
  • Ultrafilter
  • Weak mixing

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