{"id":"https://openalex.org/W2592828533","doi":"https://doi.org/10.1112/jlms/jdu035","title":"On the normality of numbers to different bases","display_name":"On the normality of numbers to different bases","publication_year":2014,"publication_date":"2014-07-23","ids":{"openalex":"https://openalex.org/W2592828533","doi":"https://doi.org/10.1112/jlms/jdu035","mag":"2592828533"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu035","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu035","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1311.0333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ver\u00f3nica Becher","orcid":null},"institutions":[{"id":"https://openalex.org/I53241121","display_name":"Fundaci\u00f3n Ciencias Exactas y Naturales","ror":"https://ror.org/05rxmkq09","country_code":"AR","type":"nonprofit","lineage":["https://openalex.org/I53241121"]},{"id":"https://openalex.org/I151201029","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59","country_code":"AR","type":"funder","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I24354313","display_name":"University of Buenos Aires","ror":"https://ror.org/0081fs513","country_code":"AR","type":"education","lineage":["https://openalex.org/I24354313"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Ver\u00f3nica Becher","raw_affiliation_strings":["Departamento de Computacio\u0301n, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires & CONICET, Pabello\u0301n I, Ciudad Universitaria, 1428 Buenos Aires, Argentina, [email protected]"],"affiliations":[{"raw_affiliation_string":"Departamento de Computacio\u0301n, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires & CONICET, Pabello\u0301n I, Ciudad Universitaria, 1428 Buenos Aires, Argentina, [email protected]","institution_ids":["https://openalex.org/I53241121","https://openalex.org/I151201029","https://openalex.org/I24354313"]}]},{"author_position":"last","author":{"id":null,"display_name":"Theodore A. Slaman","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Theodore A. Slaman","raw_affiliation_strings":["Department of Mathematics, The University of California, Berkeley, 719 Evans Hall #3840, Berkeley, CA 94720-3840, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of California, Berkeley, 719 Evans Hall #3840, Berkeley, CA 94720-3840, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":1.8727,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85666976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"90","issue":"2","first_page":"472","last_page":"494"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.3140000104904175,"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":0.3140000104904175,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.17730000615119934,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.06620000302791595,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/multiplicative-function","display_name":"Multiplicative function","score":0.6977999806404114},{"id":"https://openalex.org/keywords/normality","display_name":"Normality","score":0.6686999797821045},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.65420001745224},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5860000252723694},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.5494999885559082},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5109000205993652},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.48890000581741333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8569999933242798},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6977999806404114},{"id":"https://openalex.org/C2776157432","wikidata":"https://www.wikidata.org/wiki/Q1375683","display_name":"Normality","level":2,"score":0.6686999797821045},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.65420001745224},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5860000252723694},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.5494999885559082},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5109000205993652},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.48890000581741333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4805000126361847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46149998903274536},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37220001220703125},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C1911482","wikidata":"https://www.wikidata.org/wiki/Q854531","display_name":"Real analysis","level":2,"score":0.25609999895095825}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/jlms/jdu035","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu035","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1311.0333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.0333","pdf_url":"https://arxiv.org/pdf/1311.0333","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.0333","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.0333","pdf_url":"https://arxiv.org/pdf/1311.0333","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":7,"referenced_works":["https://openalex.org/W1447601445","https://openalex.org/W1557463835","https://openalex.org/W1597033183","https://openalex.org/W2035706983","https://openalex.org/W2044995436","https://openalex.org/W2055910828","https://openalex.org/W6696009978"],"related_works":[],"abstract_inverted_index":{"We":[0,74],"demonstrate":[1],"the":[2,15,42,58,62,78,111],"full":[3],"logical":[4],"independence":[5],"of":[6,17,44,61,94],"normality":[7],"to":[8,19,30,50,107,118],"multiplicatively":[9,82],"independent":[10,83],"bases.":[11],"This":[12,124],"establishes":[13,40],"that":[14,41,77,104],"set":[16,43,93],"bases":[18,84,95],"which":[20,47,65],"a":[21,126],"real":[22,45,102],"number":[23],"can":[24],"be":[25],"normal":[26,49,106,117],"is":[27,55],"not":[28,115],"tied":[29],"any":[31,91,119],"arithmetical":[32],"properties":[33],"other":[34],"than":[35],"multiplicative":[36,98],"dependence.":[37],"It":[38],"also":[39],"numbers":[46,103],"are":[48,85,101,105],"at":[51,57],"least":[52],"one":[53],"base":[54,109,120],"properly":[56],"fourth":[59],"level":[60],"Borel":[63],"hierarchy,":[64],"was":[66],"conjectured":[67],"by":[68,130],"A.":[69],"Ditzen":[70],"20":[71],"years":[72],"ago.":[73],"further":[75],"show":[76],"discrepancy":[79],"functions":[80],"for":[81,90],"pairwise":[86],"independent.":[87],"In":[88],"addition,":[89],"given":[92,112],"closed":[96],"under":[97],"dependence,":[99],"there":[100],"each":[108],"in":[110,121],"set,":[113],"but":[114],"simply":[116],"its":[122],"complement.":[123],"answers":[125],"question":[127],"first":[128],"raised":[129],"Brown,":[131],"Moran":[132],"and":[133],"Pearce.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2017-03-16T00:00:00"}