We prove the L2-convergence for the linear multiple ergodic averages of commuting transformations T1,..., T2), assuming that each map 7i and each pair 7iT j-1 is ergodic for i ≠ j. The limiting behavior of such averages is controlled by a particular factor, which is an inverse limit of nilsystems. As a corollary we show that the limiting behavior of linear multiple ergodic averages is the same for commuting transformations.
ASJC Scopus subject areas
- Applied Mathematics