  Let $\Gamma$ be the fundamental group of a finite connected graph $\mathcal
G$. Let $\mathfrak M$ be an abelian group. A {\it distribution} on the boundary
$\partial\Delta$ of the universal covering tree $\Delta$ is an $\mathfrak
M$-valued measure defined on clopen sets. If $\mathfrak M$ has no
$\chi(\mathcal G)$-torsion then the group of $\Gamma$-invariant distributions
on $\partial\Delta$ is isomorphic to $H_1(\mathcal G,\mathfrak M)$.
