Pointwise density topology
The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue...
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De Gruyter
2015-01-01
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| Series: | Open Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/math.2015.13.issue-1/math-2015-0008/math-2015-0008.xml?format=INT |
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doaj-ca4543f832ff41beb7f73122f8efcd662020-11-24T22:02:42ZengDe GruyterOpen Mathematics2391-54552015-01-0113110.1515/math-2015-0008math-2015-0008Pointwise density topologyGórajska Magdalena0Centre of Mathematics and Physics, Lodz University of Technology, Politechniki 22, 90-924 Lodz, PolandThe paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable.http://www.degruyter.com/view/j/math.2015.13.issue-1/math-2015-0008/math-2015-0008.xml?format=INTDensity pointDensity topologyPointwise convergence |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Górajska Magdalena |
| spellingShingle |
Górajska Magdalena Pointwise density topology Open Mathematics Density point Density topology Pointwise convergence |
| author_facet |
Górajska Magdalena |
| author_sort |
Górajska Magdalena |
| title |
Pointwise density topology |
| title_short |
Pointwise density topology |
| title_full |
Pointwise density topology |
| title_fullStr |
Pointwise density topology |
| title_full_unstemmed |
Pointwise density topology |
| title_sort |
pointwise density topology |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2015-01-01 |
| description |
The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable. |
| topic |
Density point Density topology Pointwise convergence |
| url |
http://www.degruyter.com/view/j/math.2015.13.issue-1/math-2015-0008/math-2015-0008.xml?format=INT |
| work_keys_str_mv |
AT gorajskamagdalena pointwisedensitytopology |
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1725834479320170496 |