  In this paper we introduce a general notion of weak extension property for
embeddings induced by a group actions. As an example, for the group H(M, m) of
measure-preserving homeomorphisms of a noncompact manifold M, we deduce weak
type extension theorems, and as an application we exhibit the local
contractibility of the group H_c(M, m) of measure-preserving homeomorphisms
with compact support of a noncompact connected manifold M endowed with the
Whitney topology.
