SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular. Avila, A., Matheus, C., & Yoccoz, J.C. Geometric and Functional Analysis, 23(6):1705--1729, 2013.
doi  bibtex   
@article{ avila_sl2r-invariant_2013,
  title = {{SL}(2,{R})-invariant probability measures on the moduli spaces of translation surfaces are regular},
  volume = {23},
  doi = {10.1007/s00039-013-0244-5},
  language = {en},
  number = {6},
  urldate = {2014-09-09},
  journal = {Geometric and Functional Analysis},
  author = {Avila, Artur and Matheus, Carlos and Yoccoz, Jean-Christophe},
  year = {2013},
  keywords = {Signe mathématique},
  pages = {1705--1729},
  annote = {lien de la fiche : http://www.ams.org/mathscinet-getitem?mr=3132901},
  file = {MathSciNet Snapshot:C\:\\Users\̧onsultation\\AppData\\Roaming\\Mozilla\\Firefox\\Profiles\\1rk8mjlp.julien\\zotero\\storage\\EB4ZVV8G\\mathscinet-getitem.html:text/html}
}

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