Integrability on Direct Limit Banach manifolds
  This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anchor ranges. 
Patrick Cabau, Fernand Pelletier
math.DG