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[{"key": "dc.contributor.advisor", "value": "Soultanis, Elefterios", "language": null, "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Vuolasto, Veikko", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2025-04-09T07:51:44Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2025-04-09T07:51:44Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2025", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/101317", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Metristen virtojen teoria pyrkii yleist\u00e4m\u00e4\u00e4n De Rhamin ideoiman ja Federerin ja Flemingin muovaaman euklidisten virtojen teorian avaruuksille ilman ennalta m\u00e4\u00e4r\u00e4tty\u00e4 sile\u00e4\u00e4 rakennetta. Keskeinen idea on korvata sile\u00e4t differentiaalimuodot Lipschitz-monikoilla. Muodollisesti metrinen virta on \u00e4\u00e4rellisen massan multilineaarinen kuvaus Lipschitz-monikkojen avaruudelta reaaliluvuille, joka toteuttaa halutut jatkuvuus- ja lokaalisuusominaisuudet.\n\nTutkielman p\u00e4\u00e4tulos on hajotelmalause asyklisille yksiulotteisille normaalivirroille. Lyhyk\u00e4isyydess\u00e4\u00e4n lause kertoo, ett\u00e4 jokainen asyklinen yksiulotteinen normaalivirta t\u00e4ydellisess\u00e4 metrisess\u00e4 avaruudessa on jonkin \u00e4\u00e4rellisen ja suoristuville injektiivisille k\u00e4yrille keskittyneen Borel-mitan indusoima. Heikenetty versio hajotelmalauseesta yleistyy kaikille yksiulotteisille normaalivirroille ja antaa siten yhteyden avaruuden k\u00e4yrien ja sen normaalivirtojen v\u00e4lille.\n\nEnsimm\u00e4isess\u00e4 luvussa kerrataan mittateorian perusteita. Luvussa kaksi k\u00e4sitell\u00e4\u00e4n metristen virtojen perusteet, ja luku kolme sis\u00e4lt\u00e4\u00e4 todistuksen normaalivirtojen kompaktisuustulokselle. Nelj\u00e4s luku esittelee k\u00e4yrien indusoimat virrat, jotka toimivat hajotelman rakennuspalasina, ja luvussa viisi tutustutaan mittoihin k\u00e4yrien avaruudella. Kuudes luku rakentuu p\u00e4\u00e4tuloksen todistuksen ymp\u00e4rille. Seitsem\u00e4nness\u00e4 luvussa todistetaan hajotelmalauseen heikompi versio kaikille yksiulotteisille normaalivirroille.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2025-04-09T07:51:44Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2025-04-09T07:51:44Z (GMT). No. of bitstreams: 0\n Previous issue date: 2025", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "85", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": null, "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "analysis in metric spaces", "language": null, "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Decomposition of normal currents in complete metric spaces", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202504093145", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": null, "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.copyright", "value": "\u00a9 The Author(s)", "language": "fi", "element": "rights", "qualifier": "copyright", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "metriset avaruudet", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.description.accessibilityfeature", "value": "unknown accessibility", "language": "en", "element": "description", "qualifier": "accessibilityfeature", "schema": "dc"}, {"key": "dc.description.accessibilityfeature", "value": "ei tietoa saavutettavuudesta", "language": "fi", "element": "description", "qualifier": "accessibilityfeature", "schema": "dc"}]
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