  We consider weak invariance principles (functional limit theorems) in the
domain of a stable law. A general result is obtained on lifting such limit laws
from an induced dynamical system to the original system. An important class of
examples covered by our result are Pomeau-Manneville intermittency maps, where
convergence for the induced system is in the standard Skorohod J_1 topology.
For the full system, convergence in the J_1 topology fails, but we prove
convergence in the M_1 topology.
