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

Amenability of semigroups and common multiples in $\ell^1_+$