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A new flavour of amenability for discrete semigroups is proposed that generalises group amenability and follows from a Følner-type condition. Some examples are explored, to argue that this new notion better captures some essential ideas of amenability. A semigroup S is left fairly amenable if, and only if, it supports a mean m∈ℓ∞(S)⁎ satisfying m(f)=m(s⁎f) whenever s⁎f∈ℓ∞(S), thus justifying the nomenclature...
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