{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86799"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86799","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Pointwise Relations Between Ergodic Averages and Martingales","abstract":"It is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale.","abstract_html":"It is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale.","abstract_has_math":false,"creators":["Goubran, Nader"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Rosenblatt, Joseph"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:36Z","date_published":"2015-09-28T15:19:36Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3070310"],"render_values":[{"text":"(MiAaPQ)AAI3070310","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86799","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rosenblatt, Joseph"]},{"key":"dc:creator","label":"Author","values":["Goubran, Nader"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:36Z","10000-01-01","2002"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86799","(MiAaPQ)AAI3070310"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["It is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale.","Made available in DSpace on 2015-09-28T15:19:36Z (GMT). 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In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale.","Made available in DSpace on 2015-09-28T15:19:36Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070310.pdf: 1833406 bytes, checksum: bc97e430fa9a6be2cb629c3cf5df920e (MD5) Previous issue date: 2002","Embargo set by: Seth Robbins for item 88080 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","51 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002."],"dc:identifier":["http://hdl.handle.net/2142/86799","(MiAaPQ)AAI3070310"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Pointwise Relations Between Ergodic Averages and Martingales"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:27Z"}