Notes on Austin's multiple ergodic theorem

Thierry de La Rue (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, extensions and factors. The existence of a sated extension, which is a key argument in the proof, is presented in a general context.

Mots clés: multiple ergodic theorem; joinings; factors; sated extension

Domaines: Systèmes dynamiques [math.DS]

Thierry de La Rue. Notes on Austin's multiple ergodic theorem. 2009. ⟨hal-00400975v4⟩