  In this note, we prove that a semigroup $S$ is left amenable if and only if
every two nonzero elements of $\ell^1_+(S)$ have a common nonzero right
multiple, where $\ell^1_+(S)$ is the positive part of the Banach algebra
$\ell^1(S)$, or equivalently the semiring of finite measures on $S$. This
characterization of amenability is new even for groups.
