Logarithmic Summability in Ergodic Theory

Sakin Demir

Dumlupınar Mah. 38. Sok. No. 23 Daire 7, Demirtaş Nah. Osmangazi, 16245, Bursa, TURKEY.


Given an ergodic, measure preserving dynamical system (X, ,, ) we prove under an additional assumption that 1 1 ( ) lim log n k n k f x fd n k        a.e. for all 1f L (X) . Another result about the behavior of the same sequence of operators has also been found. Mathematics Subject Classification: 37A30, 28D05, 47A35.

Keywords :Logarithmic Summabilty, Ergodic Theory.

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