A ratio ergodic theorem for Borel actions of ℤd×ℝk

DOI10.1017/S0143385711001076zbMath1251.37006OpenAlexW2051151113MaRDI QIDQ2908153

Eric Norman Holt

Publication date: 4 September 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385711001076

zbMATH Keywords

Følner conditionBesicovitch covering lemmaratio ergodic theoremfree Borel actionHochman lemmaRudolph's diffusion

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (2)

HT90 and ``simplest number fields ⋮ Ergodic theorems for capacity preserving \(\mathbb{Z}_+^d\)-actions

Cites Work

• A ratio ergodic theorem for multiparameter non-singular actions
• On the ergodic theorem of Hurewicz
• Ergodic theorem without invariant measure
• A ratio ergodic theorem for commuting, conservative, invertible transformations with quasi-invariant measure summed over symmetric hypercubes
• The ergodic and entropy theorems revisited
• Proof of the Ergodic Theorem

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