an:04082338
Zbl 0662.47006
Bourgain, J.
An approach to pointwise ergodic theorems
EN
Geometric aspects of functional analysis, Isr. Semin. 1986-87, Lect. Notes Math. 1317, 204-223 (1988).
1988
a
47A35 28D05
individual ergodic theorem; dynamical system; ergodic means
[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 \(f\in L^ 2(\Omega,\mu)\).
A.A.Mekler
Zbl 0638.00019