Abstract

Logarithmic Summability in Ergodic Theory

Sakin Demir

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

ABSTRACT

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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