# Measure rigidity for leafwise weakly rigid actions

@article{Ponce2018MeasureRF, title={Measure rigidity for leafwise weakly rigid actions}, author={Gabriel Ponce and R'egis Varao}, journal={arXiv: Dynamical Systems}, year={2018} }

Given a Borel action $G\curvearrowright X$ over a Lebesgue space $X$ we show that if $G\curvearrowright X$ preserves an invariant system of packing regular metrics along a Borel lamination $\mathcal F$, then the ergodic measures preserved by the action are rigid in the sense that the system of conditional measures with respect to the partition $\mathcal F$ are induced by the given invariant metric system or are supported in a countable number of boundaries of balls. The argument we employ does…

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