In this paper a comparison
is made between c-density and k-density in the general setting of Freedman
density spaces in additive number theory. The comparison is motivated by the
following question of Freedman: Does there exist a density space and a set
such that the c-density of that set is positive and the k-density is zero?
The answer is yes. More generally, there exists a density space such that
for any two real numbers ρ1 and ρ2 with 0 ≦ ρ1≦ ρ2< 1, a set can be
constructed such that the k-density of the set is ρ1 while the c-density is
ρ2.
