English

Ratio ergodic theorems: From Hopf to Birkhoff and Kingman

Dynamical Systems 2018-02-26 v1 Probability

Abstract

Hopf's ratio ergodic theorem has an inherent symmetry which we exploit to provide a simplification of standard proofs of Hopf's and Birkhoff's ergodic theorems. We also present a ratio ergodic theorem for conservative transformations on a σ\sigma-finite measure space, generalizing Kingman's ergodic theorem for subadditive sequences and generalizing previous results by Akcoglu and Sucheston.

Keywords

Cite

@article{arxiv.1802.08439,
  title  = {Ratio ergodic theorems: From Hopf to Birkhoff and Kingman},
  author = {Hans Henrik Rugh and Damien Thomine},
  journal= {arXiv preprint arXiv:1802.08439},
  year   = {2018}
}