WM groups and Ramsey theory

Vitaly Bergelson, Hillel Furstenberg

Research output: Contribution to journalArticlepeer-review


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
Issue number16
StatePublished - 1 Oct 2009
Externally publishedYes

Bibliographical note

Funding Information:
E-mail addresses: vitaly@math.ohio-state.edu (V. Bergelson), harry@math.huji.ac.il (H. Furstenberg). 1 The first author was supported by NSF grant DMS-0600042.


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


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