Ergodic Theory of the Space of Measured Laminations

@article{Lindenstrauss2010ErgodicTO,
  title={Ergodic Theory of the Space of Measured Laminations},
  author={Elon Lindenstrauss and Maryam Mirzakhani},
  journal={International Mathematics Research Notices},
  year={2010},
  volume={2008}
}
We classify locally finite invariant measures and orbit closure for the action of the mapping class group on the space of measured laminations on a surface. This classification translates to a classification of measures and orbit closures on the space of quadratic differentials invariant under the horospheric foliation. 

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