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An approach to pointwise ergodic theorems. (English) Zbl 0662.47006
Geometric aspects of functional analysis, Isr. Semin. 1986-87, Lect. Notes Math. 1317, 204-223 (1988).

[For the entire collection see Zbl 0638.00019.]

Continuing his previous investigations of the individual ergodic theorem the author states the following

Theorem 1. Let (${\Omega }$,$ℬ,\mu ,T\right)$ be a dynamical system. Denoting ${𝔓}_{N}=\left\{p|p=prime\le N\right\}$ and $|{𝔓}_{N}|$ its cardinality, the ergodic means

${A}_{N}f={|{𝔓}_{N}|}^{-1}\sum _{p\in {𝔓}_{N}}{T}^{p}f$

converge almost surely for $f\in {L}^{2}\left({\Omega },\mu \right)$.

Reviewer: A.A.Mekler

##### MSC:
 47A35 Ergodic theory of linear operators 28D05 Measure-preserving transformations