Multiple ergodic theorems

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Given measure preserving transformations T 1, T 2,..., T s of a probability space (X, B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form {Mathematical expression} where f 1, f 2,..., f s e{open}L(X, B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) in L 2-norm is ∫ x f 1 dμ·∫ x f 2 dμ...∫ x f s dμ for any f 1, f 2..., f s e{open}L(X, B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.

Original languageEnglish
Pages (from-to)123-142
Number of pages20
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - 1 Dec 1988

ASJC Scopus subject areas

  • Analysis
  • Mathematics (all)


Dive into the research topics of 'Multiple ergodic theorems'. Together they form a unique fingerprint.

Cite this