Vol. 48, No. 1, 1973

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A comparison of c-density and k-density

Arthur E. Olson

Vol. 48 (1973), No. 1, 209–213

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.

Mathematical Subject Classification
Primary: 10L10
Received: 22 June 1972
Published: 1 September 1973
Arthur E. Olson