Finitely additive measures on N

AbstractWe study finitely additive measures on N, in particular how nice such a measure can be. We would like our “nice” measures to satisfy the following demand: If Y is obtained from X by a process which makes sets r times as small, from an intuitive point of view, thenμ(Y)=r-1·μ(X) for all X, YϵP(N). Our measures show that formally distinct ways of making this statement precise are, indeed, distinct. One of our measures is extremely nice; it will be used to study the intuitively correct size of subsets of N