Almost Sure Convergence of the Multiple Ergodic Average for Certain Weakly Mixin

2018年第1期

关键词:
Multiple ergodic average;PID;Rokhlin con

Keywords
Multiple ergodic average;PID;Rokhlin conjecture
摘要
     The family of pairwise independently determined(PID) systems, i.e., those for which the independent joining is the only self joining with independent 2-marginals, is a class of systems for which the long standing open question by Rokhlin, of whether mixing implies mixing of all orders, has a positive answer. We show that in the class of weakly mixing PID one finds a positive answer for another long-standing open problem, whether the multiple ergodic averages 1/N N-1∑n=0 f1(Tnx)···fd(Tdnx),N→∞,almost surely converge.


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