Abstract: 
Suppose $M$ is a noncompact connected $n$-manifold and $\omega$ 
is a good Radon measure of $M$ with $\omega(\partial M) = 0$. 
Let ${\cal H}(M, \omega)$ denote the group 
of $\omega$-preserving homeomorphisms of $M$ 
equipped with the compact-open topology, 
and ${\cal H}_E(M, \omega)$ the subgroup consisting 
of all $h \in {\cal H}(M, \omega)$ which fix the ends of $M$. 
 S.~R.~Alpern and V. S. Prasad introduced 
the topological vector space ${\cal S}(M, \omega)$ of end charges of $M$ and 
the end charge homomorphism $c^\omega : {\cal H}_E(M, \omega) \to 
{\cal S}(M, \omega)$, 
which measures for each $h \in {\cal H}_E(M, \omega)$ the mass 
flow toward ends induced by~$h$. 
 We show that the map $c^\omega$ has a continuous section. 
This induces the factorization ${\cal H}_E(M, \omega) \cong 
{\rm Ker}\,c^\omega \times {\cal S}(M, \omega)$ 
and implies that ${\rm Ker}\,c^\omega$ is a strong 
deformation retract of ${\cal H}_E(M, \omega)$.

1. Division of Mathematics
   Faculty of Engineering and Design
   Kyoto Institute of Technology
   Matsugasaki, Sakyoku, Kyoto 606-8585, Japan