Type: Article
Publication Date: 2019-09-03
Citations: 3
DOI: https://doi.org/10.1007/s00041-019-09695-9
Given an ergodic dynamical system $$(X, \mathcal {B}, \mu , T)$$, we prove that for each function f belonging to the Orlicz space $$L(\log L)^2(\log \log L)(X, \mu )$$, the ergodic averages $$\begin{aligned} \frac{1}{\pi (N)} \sum _{p \in \mathbb {P}_N} f\big (T^p x\big ), \end{aligned}$$converge for $$\mu $$-almost all $$x \in X$$, where $$\mathbb {P}_N$$ is the set of prime numbers not larger that N and $$\pi (N) = \# \mathbb {P}_N$$.