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

Lewis Bowen, Peter Burton

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…