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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 ($$\Omega$$,$${\mathcal B},\mu,T)$$ be a dynamical system. Denoting $${\mathfrak P}_ N=\{p| p=prime\leq N\}$$ and $$| {\mathfrak P}_ N|$$ its cardinality, the ergodic means $A_ Nf=| {\mathfrak P}_ N|^{-1}\sum_{p\in {\mathfrak P}_ N}T^ pf$ converge almost surely for $$f\in L^ 2(\Omega,\mu)$$.
Reviewer: A.A.Mekler

##### MSC:
 47A35 Ergodic theory of linear operators 28D05 Measure-preserving transformations
##### Keywords:
individual ergodic theorem; dynamical system; ergodic means