Ergodic theorem and algorithmic randomness
Dynamical Systems
2023-06-23 v1 Logic
Probability
Abstract
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the effective ergodic theorem in general).
Cite
@article{arxiv.2306.12769,
title = {Ergodic theorem and algorithmic randomness},
author = {Alexander Shen},
journal= {arXiv preprint arXiv:2306.12769},
year = {2023}
}
Comments
Russian version appended