Abstract
In this note, we will prove that for commuting ergodic measure preserving transformationsR, S andT, ifRT −1,ST −1 are also ergodic, then the limit
exists inL 1-norm. The method used in this note was developed byConze, Furstenberg, Lesigne andWeiss.
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Zhang, Q. On convergence of the averages\(\frac{1}{N}\sum\nolimits_{n = 1}^N {f_1 (R^n x)f_2 (S^n x)f_3 (T^n x)} \) . Monatshefte für Mathematik 122, 275–300 (1996). https://doi.org/10.1007/BF01320190
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DOI: https://doi.org/10.1007/BF01320190