Geodesic
On the sequence of integer parts of a good sequence for the ergodic theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 737-743.

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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.
Classification : 28D10, 40A30, 60F25
Keywords: ergodic theorem along subsequences; Banach principle 
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Lesigne, Emmanuel. On the sequence of integer parts of a good sequence for the ergodic theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 737-743. http://geodesic.mathdoc.fr/item/CMUC_1995__36_4_a11/