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 \(p=1\).

中文翻译：

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$$\mathrm {PSL}_2(\mathbb {R})$$ PSL 2 ( R ) 的 $$L^1$$ L 1 逐点遍历定理的失败

Amos Nevo 建立了 \(L^p\) 中的逐点遍历定理，用于在概率空间上关于球平均值和每个 \( p>1\)。本文通过明确的例子表明，Nevo 定理不能推广到 \(p=1\)。