Convergence of Multiple Ergodic Averages for Some Commuting Transformations
نویسنده
چکیده
We prove the L convergence for the linear multiple ergodic averages of commuting transformations T1, . . . , Tl, assuming that each map Ti and each pair TiT −1 j is ergodic for i 6= 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.
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