On convergence of the averages \({1\over N}\sum_{n=1}^N f_1(R^nx)f_2(S^nx)f_3(T^nx)\)

DOI10.1007/BF01320190zbMath0911.28012OpenAlexW2072038186MaRDI QIDQ1364386

O. Diekmann

Publication date: 23 April 1999

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178748

zbMATH Keywords

commuting measure-preserving transformationdiagonal measuresmultiple ergodic theorems

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) General groups of measure-preserving transformations (28D15) Entropy and other invariants (28D20)

Related Items (12)

Some open problems on multiple ergodic averages ⋮ Norm convergence of continuous-time polynomial multiple ergodic averages ⋮ Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions ⋮ The Brin Prize works of Tim Austin ⋮ Deducing the multidimensional Szemerédi theorem from an infinitary removal lemma ⋮ Norm convergence of nilpotent ergodic averages ⋮ Norm convergence of multiple ergodic averages for commuting transformations ⋮ On the norm convergence of non-conventional ergodic averages ⋮ A non-singular dynamical system without maximal ergodic inequality ⋮ Convergence of diagonal ergodic averages ⋮ Pleasant extensions retaining algebraic structure. I ⋮ Pleasant extensions retaining algebraic structure. II

Cites Work

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• Extensions of ergodic group actions
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Théorèmes ergodiques pour des mesures diagonales
• Résolution d'une équation fonctionnelle
• Weakly mixing PET
• Théorèmes ergodiques pour une translation sur un nilvariété
• Double recurrence and almost sure convergence.

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