This HTML5 document contains 65 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dbpedia-dehttp://de.dbpedia.org/resource/
dcthttp://purl.org/dc/terms/
yago-reshttp://yago-knowledge.org/resource/
dbohttp://dbpedia.org/ontology/
foafhttp://xmlns.com/foaf/0.1/
n18https://global.dbpedia.org/id/
yagohttp://dbpedia.org/class/yago/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
freebasehttp://rdf.freebase.com/ns/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
wikipedia-enhttp://en.wikipedia.org/wiki/
dbchttp://dbpedia.org/resource/Category:
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Izabella_Łaba
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
Subject Item
dbr:Erdős_distinct_distances_problem
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
Subject Item
dbr:Distance_set
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
Subject Item
dbr:Falconer_distance_problem
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
dbo:wikiPageRedirects
dbr:Falconer's_conjecture
Subject Item
dbr:Falconer's_conjecture
rdf:type
yago:Concept105835747 yago:Speculation105891783 yago:Content105809192 yago:PsychologicalFeature100023100 yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Hypothesis105888929 yago:Idea105833840
rdfs:label
Falconer's conjecture Vermutung von Falconer
rdfs:comment
In der Mathematik ist die Vermutung von Falconer eine 1985 von Kenneth J. Falconer aufgestellte Vermutung, die beantworten soll, wie groß die Dimension einer Menge sein muss, damit die Menge ihrer Abstände positives Volumen hat. Sie verallgemeinert den Satz von Steinhaus. Die Vermutung von Falconer besagt, dass für eine kompakte Menge der Hausdorff-Dimension größer als die Menge positives Lebesgue-Maß hat. In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact -dimensional spaces. Intuitively, it states that a set of points that is large in its Hausdorff dimension must determine a set of distances that is large in measure. More precisely, if is a compact set of points in -dimensional Euclidean space whose Hausdorff dimension is strictly greater than , then the conjecture states that the set of distances between pairs of points in must have nonzero Lebesgue measure.
dct:subject
dbc:Unsolved_problems_in_geometry dbc:Measure_theory dbc:Dimension_theory dbc:Metric_geometry dbc:Conjectures
dbo:wikiPageID
38368203
dbo:wikiPageRevisionID
1099330414
dbo:wikiPageWikiLink
dbr:Real_number dbr:Compact_set dbr:Euclidean_distance dbr:Erdős_distinct_distances_problem dbr:Measure_(mathematics) dbr:Distance_set dbr:Kenneth_Falconer_(mathematician) dbr:Euclidean_plane dbr:Geometric_measure_theory dbc:Measure_theory dbr:Hausdorff_dimension dbr:Hugo_Steinhaus dbc:Unsolved_problems_in_geometry dbc:Dimension_theory dbr:Paul_Erdős dbr:Kakeya_set dbr:Lebesgue_measure dbr:Subring dbr:Steinhaus_theorem dbr:Difference_set dbc:Metric_geometry dbc:Conjectures dbr:Borel_set
owl:sameAs
freebase:m.0qftl_g dbpedia-de:Vermutung_von_Falconer wikidata:Q5431790 yago-res:Falconer's_conjecture n18:4jVuR
dbp:wikiPageUsesTemplate
dbt:Reflist dbt:Harvtxt
dbo:abstract
In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact -dimensional spaces. Intuitively, it states that a set of points that is large in its Hausdorff dimension must determine a set of distances that is large in measure. More precisely, if is a compact set of points in -dimensional Euclidean space whose Hausdorff dimension is strictly greater than , then the conjecture states that the set of distances between pairs of points in must have nonzero Lebesgue measure. In der Mathematik ist die Vermutung von Falconer eine 1985 von Kenneth J. Falconer aufgestellte Vermutung, die beantworten soll, wie groß die Dimension einer Menge sein muss, damit die Menge ihrer Abstände positives Volumen hat. Sie verallgemeinert den Satz von Steinhaus. Die Vermutung von Falconer besagt, dass für eine kompakte Menge der Hausdorff-Dimension größer als die Menge positives Lebesgue-Maß hat.
prov:wasDerivedFrom
wikipedia-en:Falconer's_conjecture?oldid=1099330414&ns=0
dbo:wikiPageLength
7446
foaf:isPrimaryTopicOf
wikipedia-en:Falconer's_conjecture
Subject Item
dbr:Kenneth_Falconer_(mathematician)
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
dbo:knownFor
dbr:Falconer's_conjecture
Subject Item
dbr:List_of_unsolved_problems_in_mathematics
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
Subject Item
dbr:Steinhaus_theorem
dbo:wikiPageWikiLink
dbr:Falconer's_conjecture
Subject Item
wikipedia-en:Falconer's_conjecture
foaf:primaryTopic
dbr:Falconer's_conjecture