We investigate some properties of density measures - finitely
additive measures on the set of natural numbers N extending
asymptotic density. We introduce a class of density measures,
which is defined using cluster points of the sequence
A(n)/n as well as cluster points of some other
similar sequences.
We obtain range of possible values of density measures for any subset of N. Our description
of this range simplifies the description of
[K. P. S. BHASKARA RAO, M. BHASKARA RAO, Theory of Charges – A Study of Finitely Additive Measures, Academic Press, London–New York, 1983.]
for general finitely additive measures.
Also the values which can be attained by the measures defined
in the first part of the paper are studied.
The answer to Problem 1 from this paper is affirmative, see here.