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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