Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Nikodym_set> ?p ?o }
Showing triples 1 to 37 of
37
with 100 triples per page.
- Nikodym_set abstract "In mathematics, a Nikodym set is the seemingly paradoxical result of a construction in measure theory. A Nikodym set in the unit square S in the Euclidean plane E2 is a subset N of S such that the area (i.e. two-dimensional Lebesgue measure) of N is 1; for every point x of N, there is a straight line through x that meets N only at x.Analogous sets also exist in higher dimensions.The existence of such a set as N was first proved in 1927, by Polish mathematician Otto M. Nikodym. The existence of higher-dimensional Nikodym sets was first proved in 1986, by British mathematician Kenneth Falconer.Nikodym sets are closely related to Kakeya sets (also known as Besicovitch sets).The existence of Nikodym sets is sometimes compared with the Banach–Tarski paradox. There is, however, an important difference between the two: the Banach–Tarski paradox relies on non-measurable sets.".
- Nikodym_set wikiPageID "14563922".
- Nikodym_set wikiPageLength "1457".
- Nikodym_set wikiPageOutDegree "19".
- Nikodym_set wikiPageRevisionID "654606636".
- Nikodym_set wikiPageWikiLink Area.
- Nikodym_set wikiPageWikiLink Banach–Tarski_paradox.
- Nikodym_set wikiPageWikiLink Category:Measure_theory.
- Nikodym_set wikiPageWikiLink Category:Paradoxes.
- Nikodym_set wikiPageWikiLink Dimension.
- Nikodym_set wikiPageWikiLink Kakeya_set.
- Nikodym_set wikiPageWikiLink Kenneth_Falconer_(mathematician).
- Nikodym_set wikiPageWikiLink Lebesgue_measure.
- Nikodym_set wikiPageWikiLink Line_(geometry).
- Nikodym_set wikiPageWikiLink London_Mathematical_Society.
- Nikodym_set wikiPageWikiLink Mathematician.
- Nikodym_set wikiPageWikiLink Mathematics.
- Nikodym_set wikiPageWikiLink Measure_(mathematics).
- Nikodym_set wikiPageWikiLink Otto_M._Nikodym.
- Nikodym_set wikiPageWikiLink Paradox.
- Nikodym_set wikiPageWikiLink Poland.
- Nikodym_set wikiPageWikiLink Subset.
- Nikodym_set wikiPageWikiLink Two-dimensional_space.
- Nikodym_set wikiPageWikiLink Unit_square.
- Nikodym_set wikiPageWikiLinkText "Nikodym set".
- Nikodym_set wikiPageUsesTemplate Template:Citation.
- Nikodym_set subject Category:Measure_theory.
- Nikodym_set subject Category:Paradoxes.
- Nikodym_set type Concept.
- Nikodym_set comment "In mathematics, a Nikodym set is the seemingly paradoxical result of a construction in measure theory. A Nikodym set in the unit square S in the Euclidean plane E2 is a subset N of S such that the area (i.e. two-dimensional Lebesgue measure) of N is 1; for every point x of N, there is a straight line through x that meets N only at x.Analogous sets also exist in higher dimensions.The existence of such a set as N was first proved in 1927, by Polish mathematician Otto M. Nikodym.".
- Nikodym_set label "Nikodym set".
- Nikodym_set sameAs Q7035471.
- Nikodym_set sameAs m.03d80lg.
- Nikodym_set sameAs Множество_Никодима.
- Nikodym_set sameAs Q7035471.
- Nikodym_set wasDerivedFrom Nikodym_set?oldid=654606636.
- Nikodym_set isPrimaryTopicOf Nikodym_set.