{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23623"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23623","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Metric entropies of various function spaces","abstract":"The metric entropy of a set is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2$\\varepsilon$ which cover the set. We calculate the asymptotic order of the metric entropy as $\\varepsilon\\ \\to {\\rm 0}\\sp{+}$ for various function spaces. Some spaces we consider are the Sobolov spaces $L\\sbsp{1}{p}$((0, 1)) for 1 $<$ $p \\leq$ 2, and spaces of smooth functions on certain Cantor-like subsets of (0, 1).","abstract_html":"The metric entropy of a set is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2$\\varepsilon$ which cover the set. We calculate the asymptotic order of the metric entropy as <span class=\"etd-inline-math\">\\varepsilon \\to {\\rm 0}\\sp{+}</span> for various function spaces. Some spaces we consider are the Sobolov spaces $L\\sbsp{1}{p}$((0, 1)) for 1 $&lt;$ $p \\leq$ 2, and spaces of smooth functions on certain Cantor-like subsets of (0, 1).","abstract_has_math":true,"creators":["Strus, Joseph Michael"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Kaufman, Robert"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:21:00Z","date_published":"2011-05-07T14:21:00Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Mathematics","Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1994 Strus, Joseph Michael"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9503333","(UMI)AAI9503333"],"render_values":[{"text":"AAI9503333","href":null,"code":true},{"text":"(UMI)AAI9503333","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23623","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kaufman, Robert"]},{"key":"dc:creator","label":"Author","values":["Strus, Joseph Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:21:00Z","10000-01-01","1994"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics","Engineering, Electronics and Electrical"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Engineering, Electronics and Electrical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1994 Strus, Joseph Michael"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9503333","(UMI)AAI9503333","http://hdl.handle.net/2142/23623"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The metric entropy of a set is a measure of its size in terms of the minimal number of sets of diameter not exceeding 2$\\varepsilon$ which cover the set. We calculate the asymptotic order of the metric entropy as $\\varepsilon\\ \\to {\\rm 0}\\sp{+}$ for various function spaces. Some spaces we consider are the Sobolov spaces $L\\sbsp{1}{p}$((0, 1)) for 1 $<$ $p \\leq$ 2, and spaces of smooth functions on certain Cantor-like subsets of (0, 1).","Made available in DSpace on 2011-05-07T14:21:00Z (GMT). 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We calculate the asymptotic order of the metric entropy as $\\varepsilon\\ \\to {\\rm 0}\\sp{+}$ for various function spaces. Some spaces we consider are the Sobolov spaces $L\\sbsp{1}{p}$((0, 1)) for 1 $<$ $p \\leq$ 2, and spaces of smooth functions on certain Cantor-like subsets of (0, 1).","Made available in DSpace on 2011-05-07T14:21:00Z (GMT). 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