{"id":{"repo_id":"penn","oai_identifier":"oai:repository.upenn.edu:20.500.14332/49818"},"canonical_url":"https://search.dev.ndltd.org/etd/penn/oai:repository.upenn.edu:20.500.14332/49818","repository":{"repo_id":"penn","name":"University of Pennsylvania","base_url":"https://repository.upenn.edu/server/oai/request"},"display":{"title":"Hadwiger Integration of Definable Functions","abstract":"This thesis denes and classies valuations on denable functionals. The intrinsic volumes are valuations on \"tame\" subsets of R^n, and by easy extension, valuations on functionals on R^n with nitely many level sets, each a \"tame\" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of denable functionals, we obtain dual classication theorems for general valuations on such functionals. We also explore integral transforms, convergence results, and applications of the Hadwiger integrals.","abstract_html":"This thesis denes and classies valuations on denable functionals. The intrinsic volumes are valuations on "tame" subsets of R^n, and by easy extension, valuations on functionals on R^n with nitely many level sets, each a "tame" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of denable functionals, we obtain dual classication theorems for general valuations on such functionals. We also explore integral transforms, convergence results, and applications of the Hadwiger integrals.","abstract_has_math":false,"creators":["Wright, Matthew"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Robert Ghrist"],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-12","date_published":"2011-08-12","updated_at":"2026-07-24T03:47:06Z","subjects":["Geometry and Topology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.upenn.edu/handle/20.500.14332/49818","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Robert Ghrist"]},{"key":"dc:creator","label":"Author","values":["Wright, Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-24T09:56:45.393"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-05-24T10:04:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2011-06-01T00:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-08-12"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation/Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Geometry and Topology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repository.upenn.edu/handle/20.500.14332/49818"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis denes and classies valuations on denable functionals. The intrinsic volumes are valuations on \"tame\" subsets of R^n, and by easy extension, valuations on functionals on R^n with nitely many level sets, each a \"tame\" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of denable functionals, we obtain dual classication theorems for general valuations on such functionals. We also explore integral transforms, convergence results, and applications of the Hadwiger integrals."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy (PhD)"]},{"key":"dc:title","label":"Title","values":["Hadwiger Integration of Definable Functions"]}]}],"canonical_facts":{"dc:contributor.advisor":["Robert Ghrist"],"dc:creator":["Wright, Matthew"],"dc:date":["2023-05-24T09:56:45.393"],"dc:date.accessioned":["2023-05-24T10:04:11Z"],"dc:date.available":["2011-06-01T00:00:00Z"],"dc:date.issued":["2011-08-12"],"dc:description.abstract":["This thesis denes and classies valuations on denable functionals. The intrinsic volumes are valuations on \"tame\" subsets of R^n, and by easy extension, valuations on functionals on R^n with nitely many level sets, each a \"tame\" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of denable functionals, we obtain dual classication theorems for general valuations on such functionals. We also explore integral transforms, convergence results, and applications of the Hadwiger integrals."],"dc:description.degree":["Doctor of Philosophy (PhD)"],"dc:identifier.uri":["https://repository.upenn.edu/handle/20.500.14332/49818"],"dc:subject":["Geometry and Topology"],"dc:title":["Hadwiger Integration of Definable Functions"],"dc:type":["Dissertation/Thesis"]},"updated_at":"2026-07-24T03:47:06Z"}