{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-9K25JP8F/22770613eb514-b-cf78567-666b4-4cb3a2/PDF","dcterms:extent":"243 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-9K25JP8F/c02a66e0-6968-4a72-b7d8-1be32400d9ec/TEXT","dcterms:extent":"24 KB"}],"edm:TimeSpan":{"@rdf:about":"2014-2024","edm:begin":{"@xml:lang":"en","#text":"2014"},"edm:end":{"@xml:lang":"en","#text":"2024"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-9K25JP8F","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-OE00UKYR"},{"@xml:lang":"sl","#text":"Matrika"}],"dcterms:issued":"2024","dc:creator":"Zmazek, Gal","dc:format":[{"@xml:lang":"sl","#text":"letnik:11"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"9 str."}],"dc:identifier":["COBISSID_HOST:209481731","ISSN:2385-8567","URN:URN:NBN:SI:doc-9K25JP8F"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"Založba Fakultete za matematiko in fiziko Univerze v Ljubljani"},"dc:subject":[{"@xml:lang":"en","#text":"Lebesgue measure"},{"@xml:lang":"sl","#text":"Lebesgueova mera"},{"@xml:lang":"en","#text":"measurable sets"},{"@xml:lang":"sl","#text":"merljive množice"},{"@xml:lang":"en","#text":"Vitali non-measurable set"},{"@xml:lang":"sl","#text":"Vitalijeva nemerljiva množica"}],"dcterms:temporal":{"@rdf:resource":"2014-2024"},"dc:title":{"@xml:lang":"sl","#text":"Vitalijeva nemerljiva množica|"},"dc:description":[{"@xml:lang":"sl","#text":"This article delves into the Lebesgue measure’s application to define measures for subsets of real numbers, addressing the introduction of Vitali’s non-measurable set, which creates a contradiction under traditional measurement theories if assumed measurable. It thoroughly examines measurable and non-measurable sets, ?$\\sigma$?-algebras, and the differentiation between Borel and Lebesgue measurable sets. The emphasis is on the identification of non-Borel measurable sets, advancing the understanding of measurement theory in mathematical spaces"},{"@xml:lang":"sl","#text":"Članek podrobno obravnava uporabo Lebesgueove mere za določanje mer podmnožic realnih števil, pri čemer naslavlja problematiko Vitalijeve nemerljive množice, ki v tradicionalnih teorijah merjenja ustvari protislovje, če jo predpostavimo za merljivo. Temeljito preučuje merljive in nemerljive množice, ?$\\sigma$?-algebre in razlikovanje med Borelovimi in Lebesgueovimi merljivimi množicami. Poudarek je na identifikaciji nemerljivih množic, ki niso Borelove, kar nadgradi razumevanje teorije merjenja v matematičnih prostorih"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-9K25JP8F","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-9K25JP8F"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-9K25JP8F/22770613eb514-b-cf78567-666b4-4cb3a2/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:dataProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-9K25JP8F/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-9K25JP8F"}}}}