Reiter condition ($\Vert \lambda (g){\mu }_n-{\mu }_n{\Vert }_1\to 0$)

For a countable discrete group, the Reiter condition requires a sequence of probability measures in ${\ell }^1(G)$ asymptotically invariant under every left translation. It is equivalent to the existence of an invariant mean and a Følner sequence. Separation by bounded functions shows that amenability gives approximate invariance simultaneously on each finite set of translations; countability makes the successive finite tests into a sequence.