Translation of the paper `Mesures stationnaires et ferm'es invariants   des espaces homog'enes I', by Y. Benoist and J.-F. Quint
  A translation of the famous paper of Benoist and Quint, `Mesures stationnaires et ferm\'es invariants des espaces homog\'enes I', Ann. Math. 174 (2011). 
Y. Benoist and J.-F. Quint, translated by Barak Weiss
math.DS