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[{"key": "dc.contributor.author", "value": "Hokkanen, Henri", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2023-09-22T06:32:48Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2023-09-22T06:32:48Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2009", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/89223", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Suoristuvat joukot k\u00e4ytt\u00e4ytyv\u00e4t usein arvattavalla tavalla. Esimerkiksi <i>m</i>-suoristuvan joukon (vaikkapa tasopolun osajoukon) projektiolle <i>m</i>-ulotteiselle avaruudelle on \"melkein varmasti\" positiivinen H<sup>m</sup> -mitta, kunhan projisoituva joukko ei ole H<sup>m</sup>-nollamittainen. Sen sijaan klassisen Besicovichin projektiolauseen mukaan t\u00e4ysin <i>m</i>-suoristumattomien joukkojen projektiot ovat melkein varmasti H<sup>m</sup>-nollamittaisia.\nT\u00e4ss\u00e4 tutkielmassa keskityt\u00e4\u00e4n samankaltaiseen kysymykseen. Ei ole nimitt\u00e4in hankala n\u00e4ytt\u00e4\u00e4, ettei H<sup>1</sup>-\u00e4\u00e4rellismittainen suoristuva tasojoukko leikkaa suoria kovinkaan monessa pisteess\u00e4. Tietysti leikkaus voi joskus olla ylinumeroituvakin, joten oikea muotoilu vaatii hieman v\u00e4ljyytt\u00e4. Siisp\u00e4 v\u00e4ite on mieluummin, ett\u00e4 leikkaus on \u00e4\u00e4rellinen \"tietyss\u00e4 mieless\u00e4\" melkein kaikille suorille. Kun t\u00e4m\u00e4 on selv\u00e4\u00e4, niin on luonnollista kysy\u00e4, kuinka t\u00e4ysin suoristumattomille joukoille k\u00e4y. T\u00e4m\u00e4 on osoittautunut hankalaksi kysymykseksi, eik\u00e4 siihen ole viel\u00e4 l\u00f6ytynyt vastausta. Sen sijaan t\u00e4ss\u00e4 tutkielmassa osoitetaan, ettei H<sup>1</sup>-\u00e4\u00e4rellismittaisuus pelk\u00e4st\u00e4\u00e4n takaa, ett\u00e4 melkein kaikki suorien leikkaukset joukon kanssa olisivat \u00e4\u00e4rellisi\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2023-09-22T06:32:48Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2023-09-22T06:32:48Z (GMT). No. of bitstreams: 0\n Previous issue date: 2009", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "76", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.title", "value": "Suorien leikkauksista H1-\u00e4\u00e4rellismittaisten tasojoukkojen kanssa", "language": "", "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-202309225232", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "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": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "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": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "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.oppiainekoodi", "value": "4041", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "matematiikka", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "mittateoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "geometria", "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"}]
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