  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 $\big(\frac{A(n)}{n}\big)$ 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 Bhashkara Rao
and Bhashkara Rao \cite{brbr} 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.
