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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm126, 49 pages, doi:10.1093/imrn/rnm126 published on January 16, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Ergodic Theory of the Space of Measured Laminations

Elon Lindenstrauss and Maryam Mirzakhani

Department of Mathematics, Fine Hall, Washington Road, Princeton, NJ 08544

Correspondence: Correspondence to be sent to: Maryam Mirzakhani, Department of Mathematics, Fine Hall, Washington Road, Princeton, NJ 08544.

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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