  Suppose M is a noncompact connected n-manifold and m is a good Radon measure
of M with m(bdry M) = 0. Let H(M; m) denote the group of m-preserving
homeomorphisms of M equipped with the compact-open topology and H_E(M; m)
denote the subgroup consisting of all h in H(M; m) which fix the ends of M.
Each h in H_E(M; m) moves mass toward ends and this quantity is measured by a
mass flow homomorphism J : H_E(M; m) -> V_m, where V_m is a topological vector
space. We show that the map J has a continuous section. This induces the
factorization H_E(M; m) cong Ker J times V_m and implies that Ker J is a strong
deformation retract of H_E(M; m).
