| Title:
|
Range of density measures (English) |
| Author:
|
Sleziak, Martin |
| Author:
|
Ziman, Miloš |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
17 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
33-50 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
asymptotic density |
| Keyword:
|
density measure |
| Keyword:
|
finitely additive measure |
| MSC:
|
11B05 |
| MSC:
|
20B27 |
| MSC:
|
28A12 |
| MSC:
|
28D05 |
| idZBL:
|
Zbl 1253.11010 |
| idMR:
|
MR2582958 |
| . |
| Date available:
|
2010-03-08T21:28:16Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137526 |
| . |
| Reference:
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