243 KB24 KB201420242024Zmazek, Galletnik:11številka:29 str.COBISSID_HOST:209481731ISSN:2385-8567URN:URN:NBN:SI:doc-9K25JP8FslZaložba Fakultete za matematiko in fiziko Univerze v LjubljaniMatrikaLebesgue measureLebesgueova merameasurable setsmerljive množiceVitali non-measurable setVitalijeva nemerljiva množicaVitalijeva nemerljiva množica|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 spacesČlanek 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 prostorihTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of Slovenia