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We investigate some properties of density measures – finitely additive measures on the set of natural numbers $\mathbb{N}$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $\left(\frac{A\left(n\right)}{n}\right)$ as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of $\mathbb{N}$. Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...