{"id":{"repo_id":"wku-diss","oai_identifier":"oai:digitalcommons.wku.edu:theses-1492"},"canonical_url":"https://search.dev.ndltd.org/etd/wku-diss/oai:digitalcommons.wku.edu:theses-1492","repository":{"repo_id":"wku-diss","name":"Western Kentucky University","base_url":"https://digitalcommons.wku.edu/do/oai/"},"display":{"title":"Lebesgue ▼-Measure and Riemann ▼-Integration","abstract":"Throughout the study of dynamic equations on time-scales, one traditionally finds many theorems involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a Mathematica program for finding the Riemann ▼-integral of a function on various time-scales is provided.","abstract_html":"Throughout the study of dynamic equations on time-scales, one traditionally finds many theorems involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a Mathematica program for finding the Riemann ▼-integral of a function on various time-scales is provided.","abstract_has_math":false,"creators":["Bjorum, Heather"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics and Computer Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-08-01T07:00:00Z","date_published":"2005-08-01T07:00:00Z","updated_at":"2026-07-24T06:07:28Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/489","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Bjorum, Heather"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics and Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/489"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Throughout the study of dynamic equations on time-scales, one traditionally finds many theorems involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a Mathematica program for finding the Riemann ▼-integral of a function on various time-scales is provided."]},{"key":"dc:title","label":"Title","values":["Lebesgue ▼-Measure and Riemann ▼-Integration"]}]}],"canonical_facts":{"dc:creator":["Bjorum, Heather"],"dc:description.abstract":["Throughout the study of dynamic equations on time-scales, one traditionally finds many theorems involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a Mathematica program for finding the Riemann ▼-integral of a function on various time-scales is provided."],"dc:identifier":["https://digitalcommons.wku.edu/theses/489"],"dc:subject":["Mathematics"],"dc:title":["Lebesgue ▼-Measure and Riemann ▼-Integration"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics and Computer Science"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:07:28Z"}