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arXiv · 1802.08439

Ratio ergodic theorems: From Hopf to Birkhoff and Kingman

Hans Henrik Rugh·Damien Thomine
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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 $\sigma$-finite measure space, generalizing Kingman's ergodic theorem for subadditive sequences and generalizing previous results by Akcoglu and Sucheston.

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Hans Henrik Rugh, Damien Thomine. 2018-02-23. Ratio ergodic theorems: From Hopf to Birkhoff and Kingman. https://arxiv.org/abs/1802.08439

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