An amenable group, in the discrete setting, is a group 
whose bounded
real-valued functions admit a positive normalized left-invariant
mean. This is a linear functional 
on those functions with 
, 
whenever 
, and 
for every 
.
Equivalently, an amenable discrete group admits a finitely additive left-invariant probability measure on all its subsets with total measure one. Finite groups have such a measure by normalized counting.
Factors.