Convergence and divergence of averages along subsequences in certain Orlicz spaces

C. M. Wedrychowicz

The classical theorem of Birkhoff states that the $T^{N}f(x)=(1/N){\sum }_{k=0}^{N-1}f({\sigma }^{k}x)$ converges almost everywhere for $x\in X$ and $f\in L^1(X)$, where $\sigma$ is a measure p…