  Let $X$ be a locally compact abelian group with countable base and let
$\mathcal W$ be a convex cone of positive numerical functions on $X$ which is
invariant under the group action and such that $(X,\mathcal W)$ is a balayage
space or (equivalently, if $1\in \mathcal W$) such that $\mathcal W$ is the set
of excessive functions of a Hunt process on $X$, $\mathcal W$ separates points,
every function in $\mathcal W$ is the supremum of its continuous minorants in
$\mathcal W$, and there exist strictly positive continuous $u,v\in \mathcal W$
such that $u/v\to 0$ at infinity.
  Assuming that there is a Green function $G>0$ for $X$ which locally satisfies
the triangle inequality $G(x,z)\wedge G(y,z)\le C G(x,y)$ (true for many L\'evy
processes), it is shown that Hunt's hypothesis (H) holds, that is, every
semipolar set is polar.
