{"id":"https://openalex.org/W2098371411","doi":"https://doi.org/10.2178/bsl/1130335207","title":"Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle","display_name":"Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle","publication_year":2005,"publication_date":"2005-12-01","ids":{"openalex":"https://openalex.org/W2098371411","doi":"https://doi.org/10.2178/bsl/1130335207","mag":"2098371411"},"language":"en","primary_location":{"id":"doi:10.2178/bsl/1130335207","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1130335207","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016634588","display_name":"Juris Stepr\u0101ns","orcid":"https://orcid.org/0000-0003-0765-4229"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Juris Stepr\u0101ns","raw_affiliation_strings":["Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada. E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada. E-mail:","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016634588"],"corresponding_institution_ids":["https://openalex.org/I192455969"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17678947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"4","first_page":"517","last_page":"525"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.9265093803405762},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.812806248664856},{"id":"https://openalex.org/keywords/null","display_name":"Null (SQL)","score":0.7166432738304138},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6841088533401489},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5218526124954224},{"id":"https://openalex.org/keywords/harmonic-measure","display_name":"Harmonic measure","score":0.4808679223060608},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4678790271282196},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43982040882110596},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.42929619550704956},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4244213104248047},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.42117536067962646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41355255246162415},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.3935900926589966},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32916533946990967},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13722676038742065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12193170189857483}],"concepts":[{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.9265093803405762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.812806248664856},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.7166432738304138},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6841088533401489},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5218526124954224},{"id":"https://openalex.org/C53688716","wikidata":"https://www.wikidata.org/wiki/Q5659270","display_name":"Harmonic measure","level":3,"score":0.4808679223060608},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4678790271282196},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43982040882110596},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.42929619550704956},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4244213104248047},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.42117536067962646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41355255246162415},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.3935900926589966},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32916533946990967},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13722676038742065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12193170189857483},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/bsl/1130335207","is_oa":false,"landing_page_url":"https://doi.org/10.2178/bsl/1130335207","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1130335207","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1130335207","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1505849144","https://openalex.org/W1506190783","https://openalex.org/W1908383131","https://openalex.org/W1974463980","https://openalex.org/W1979597968","https://openalex.org/W1979653193","https://openalex.org/W1983455865","https://openalex.org/W1996045241","https://openalex.org/W2004082493","https://openalex.org/W2055693724","https://openalex.org/W2059886895","https://openalex.org/W2064755890","https://openalex.org/W2072707562","https://openalex.org/W2080252880","https://openalex.org/W2099965717","https://openalex.org/W2128388094","https://openalex.org/W2169737252","https://openalex.org/W4241558944"],"related_works":["https://openalex.org/W1979009627","https://openalex.org/W1972832342","https://openalex.org/W1977410499","https://openalex.org/W2073803215","https://openalex.org/W1965393501","https://openalex.org/W2942292628","https://openalex.org/W4235175322","https://openalex.org/W1969439884","https://openalex.org/W4386588493","https://openalex.org/W3154487361"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,19,32],"shown":[3],"to":[4],"be":[5,38],"consistent":[6],"with":[7],"set":[8,12],"theory":[9],"that":[10],"every":[11],"of":[13,15,55],"reals":[14],"size":[16],"\u2135":[17,24],"1":[18,25],"null":[20],"yet":[21],"there":[22],"are":[23],"planes":[26],"in":[27],"Euclidean":[28],"3-space":[29],"whose":[30],"union":[31],"not":[33],"null.":[34],"Similar":[35],"results":[36,48],"will":[37],"obtained":[39],"for":[40],"other":[41],"geometric":[42],"objects.":[43],"The":[44],"proof":[45],"relies":[46],"on":[47],"from":[49],"harmonic":[50,57],"analysis":[51],"about":[52],"the":[53],"boundedness":[54],"certain":[56],"functions":[58],"and":[59],"a":[60],"measure":[61],"theoretic":[62],"pigeonhole":[63],"principle.":[64]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}