Corpus ID: 119320270

Measure rigidity for leafwise weakly rigid actions

  title={Measure rigidity for leafwise weakly rigid actions},
  author={Gabriel Ponce and R'egis Varao},
  journal={arXiv: Dynamical Systems},
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… Expand
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