{"id":"https://openalex.org/W2005783737","doi":"https://doi.org/10.1137/090770205","title":"On the Transport Dimension of Measures","display_name":"On the Transport Dimension of Measures","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2005783737","doi":"https://doi.org/10.1137/090770205","mag":"2005783737"},"language":"en","primary_location":{"id":"doi:10.1137/090770205","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090770205","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0905.3837","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076046596","display_name":"Qinglan Xia","orcid":"https://orcid.org/0000-0002-0263-7983"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Qinglan Xia","raw_affiliation_strings":["University of California at Davis, Department of Mathematics, Davis,CA,95616"],"affiliations":[{"raw_affiliation_string":"University of California at Davis, Department of Mathematics, Davis,CA,95616","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022083237","display_name":"Anna Vershynina","orcid":"https://orcid.org/0000-0001-5108-1531"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anna Vershynina","raw_affiliation_strings":["University of California at Davis, Department of Mathematics, Davis,CA,95616"],"affiliations":[{"raw_affiliation_string":"University of California at Davis, Department of Mathematics, Davis,CA,95616","institution_ids":["https://openalex.org/I84218800"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076046596"],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":null,"apc_paid":null,"fwci":1.7548,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.85744205,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"6","first_page":"2407","last_page":"2430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10570","display_name":"Drug Transport and Resistance Mechanisms","score":0.9740999937057495,"subfield":{"id":"https://openalex.org/subfields/2730","display_name":"Oncology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9639999866485596,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.8196096420288086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8000613451004028},{"id":"https://openalex.org/keywords/minkowski\u2013bouligand-dimension","display_name":"Minkowski\u2013Bouligand dimension","score":0.7501668930053711},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.735088586807251},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7250680327415466},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.7179273962974548},{"id":"https://openalex.org/keywords/packing-dimension","display_name":"Packing dimension","score":0.682893693447113},{"id":"https://openalex.org/keywords/dimension-function","display_name":"Dimension function","score":0.6562498211860657},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6109296083450317},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5565000772476196},{"id":"https://openalex.org/keywords/inductive-dimension","display_name":"Inductive dimension","score":0.5343595743179321},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.4950932562351227},{"id":"https://openalex.org/keywords/effective-dimension","display_name":"Effective dimension","score":0.48447656631469727},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.45946478843688965},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.45945224165916443},{"id":"https://openalex.org/keywords/hausdorff-measure","display_name":"Hausdorff measure","score":0.4289892017841339},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3679462671279907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3386993110179901},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.2570776343345642},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18811196088790894},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14171424508094788},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.12175866961479187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06821295619010925}],"concepts":[{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.8196096420288086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8000613451004028},{"id":"https://openalex.org/C101597101","wikidata":"https://www.wikidata.org/wiki/Q2555655","display_name":"Minkowski\u2013Bouligand dimension","level":4,"score":0.7501668930053711},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.735088586807251},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7250680327415466},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.7179273962974548},{"id":"https://openalex.org/C80661125","wikidata":"https://www.wikidata.org/wiki/Q5404299","display_name":"Packing dimension","level":5,"score":0.682893693447113},{"id":"https://openalex.org/C28235433","wikidata":"https://www.wikidata.org/wiki/Q5277259","display_name":"Dimension function","level":3,"score":0.6562498211860657},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6109296083450317},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5565000772476196},{"id":"https://openalex.org/C66844729","wikidata":"https://www.wikidata.org/wiki/Q841816","display_name":"Inductive dimension","level":5,"score":0.5343595743179321},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.4950932562351227},{"id":"https://openalex.org/C115311070","wikidata":"https://www.wikidata.org/wiki/Q5347255","display_name":"Effective dimension","level":3,"score":0.48447656631469727},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.45946478843688965},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.45945224165916443},{"id":"https://openalex.org/C73225184","wikidata":"https://www.wikidata.org/wiki/Q1591095","display_name":"Hausdorff measure","level":3,"score":0.4289892017841339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3679462671279907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3386993110179901},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.2570776343345642},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18811196088790894},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14171424508094788},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.12175866961479187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06821295619010925},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/090770205","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090770205","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0905.3837","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0905.3837","pdf_url":"https://arxiv.org/pdf/0905.3837","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.8077","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.8077","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.ucdavis.edu/~qlxia/Research/dimension.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.6299","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.6299","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0905.3837v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.250.8907","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.8907","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0905.3837v2.pdf","raw_type":"text"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt1nk7f4xv","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/1nk7f4xv","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:qt1nk7f4xv","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/1nk7f4xv","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Xia, Qinglan; &amp; Vershynina, Anna. (2009). On the transport dimension of measures. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/1nk7f4xv","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0905.3837","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0905.3837","pdf_url":"https://arxiv.org/pdf/0905.3837","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W618245743","https://openalex.org/W1964150502","https://openalex.org/W1978501972","https://openalex.org/W1979517512","https://openalex.org/W1983251615","https://openalex.org/W2004834853","https://openalex.org/W2009469681","https://openalex.org/W2010491857","https://openalex.org/W2011461406","https://openalex.org/W2050551798","https://openalex.org/W2054013340","https://openalex.org/W2084952261","https://openalex.org/W2114753568","https://openalex.org/W2137432509","https://openalex.org/W2163649287","https://openalex.org/W2955780226"],"related_works":["https://openalex.org/W3139576154","https://openalex.org/W2340862118","https://openalex.org/W2500320410","https://openalex.org/W4288481336","https://openalex.org/W3216690628","https://openalex.org/W2354845264","https://openalex.org/W2951592014","https://openalex.org/W2918228419","https://openalex.org/W2000583998","https://openalex.org/W3022928904"],"abstract_inverted_index":{"In":[0],"this":[1,74],"article,":[2],"we":[3,45,76],"define":[4],"the":[5,21,32,38,42,54,68,79,87],"transport":[6,22,69,80],"dimension":[7,23,34,40,81],"of":[8,24,41,56,82],"probability":[9,26,57,84,95],"measures":[10,58],"on":[11,53,59],"$\\mathbb{R}^m$":[12],"using":[13],"ramified":[14],"optimal":[15],"transportation":[16],"theory.":[17],"We":[18],"show":[19,77],"that":[20,78],"a":[25,47,64,83],"measure":[27,85],"is":[28],"bounded":[29],"above":[30],"by":[31,37],"Minkowski":[33],"and":[35],"below":[36],"Hausdorff":[39],"measure.":[43,96],"Moreover,":[44],"introduce":[46],"metric,":[48,75],"called":[49],"\u201cthe":[50],"dimensional":[51],"distance,\u201d":[52],"space":[55],"$\\mathbb{R}^m$.":[60],"This":[61],"metric":[62],"gives":[63],"geometric":[65],"meaning":[66],"to":[67,73,91],"dimension:":[70],"with":[71],"respect":[72],"equals":[86],"distance":[88],"from":[89],"it":[90],"any":[92],"finite":[93],"atomic":[94]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
