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arXiv · 1901.01299

Failure of the $L^1$ pointwise ergodic theorem for $\mathrm{PSL}_2(\mathbb{R})$

Lewis Bowen·Peter Burton
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Abstract

Amos Nevo established the pointwise ergodic theorem in $L^p$ for measure-preserving actions of $\mathrm{PSL}_2(\mathbb{R})$ on probability spaces with respect to ball averages and every $p>1$. This paper shows by explicit example that Nevo's Theorem cannot be extended to $p=1$.

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Lewis Bowen, Peter Burton. 2019-01-04. Failure of the $L^1$ pointwise ergodic theorem for $\mathrm{PSL}_2(\mathbb{R})$. https://arxiv.org/abs/1901.01299

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