Geodesic
Range of density measures
Communications in Mathematics, Tome 17 (2009) no. 1, pp. 33-50.

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We investigate some properties of density measures – finitely additive measures on the set of natural numbers $\text{$\mathbb {N}$}$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence $\bigl (\frac{A(n)}{n}\bigr )$ as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of $\text{$\mathbb {N}$}$. Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao, M., 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.
Classification : 11B05, 20B27, 28A12, 28D05
Keywords: asymptotic density; density measure; finitely additive measure 
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Sleziak, Martin; Ziman, Miloš. Range of density measures. Communications in Mathematics, Tome 17 (2009) no. 1, pp. 33-50. http://geodesic.mathdoc.fr/item/COMIM_2009__17_1_a4/