  Suppose M is a noncompact connected 2-manifold and m is a good Radon measure
of M with m(partial M) = 0. Let H(M)_0 denote the identity component of the
group of homeomorphisms of M equipped with the compact-open topology and let
H(M; m)_0 denote the identity component of the subgroup consisting of
m-preserving homeomorphisms of M. We use results of A.Fathi and R.Berlanga to
show that H(M; m)_0 is a strong deformation retract of H(M)_0 and classify the
topological type of H(M; m)_0.
