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Keywords:
ergodic theorem along subsequences; Banach principle
ergodic theorem along subsequences; Banach principle
Summary:
If $(u_n)$ is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts $([u_n])$ good for the ergodic theorem\,? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
References:
[1] Bergelson V., Boshernitzan M., Bourgain J.: Some results on non-linear recurrence. J. d'Analyse Math. 62 (1994), 29-46. MR 1269198
[2] Boshernitzan M., Jones R., Wierdl M.: Integer and fractional parts of good averaging sequences in ergodic theory. preprint, 1994. MR 1412600 | Zbl 0865.28011
[3] Bourgain J.: Almost sure convergence and bounded entropy. Israel J. Math. 63 (1988), 79-97. MR 0959049 | Zbl 0677.60042
[4] Garsia A.: Topics in Almost Everywhere Convergence. Lectures in Advanced Mathematics 4, 1970. MR 0261253 | Zbl 0198.38401
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