{"id":"https://openalex.org/W7223671004","doi":"https://doi.org/10.5281/zenodo.23675659","title":"THE FIRST JONES PROBLEM A CANTOR SET OF POSITIVE MEASURE","display_name":"THE FIRST JONES PROBLEM A CANTOR SET OF POSITIVE MEASURE","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7223671004","doi":"https://doi.org/10.5281/zenodo.23675659"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23675659","doi":"https://doi.org/10.5281/zenodo.23675659","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23675659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23675659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133582014","display_name":"Claudemir Cavalcante","orcid":"https://orcid.org/0009-0007-4426-1869","observed_orcids":["https://orcid.org/0009-0007-4426-1869"]},"institutions":[{"id":"https://openalex.org/I59606676","display_name":"Universidade Federal do Par\u00e1","ror":"https://ror.org/03q9sr818","country_code":"BR","type":"education","lineage":["https://openalex.org/I59606676"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Cavalcante, Claudemir","raw_affiliation_strings":["Universidade Federal do Par\u00e1"],"raw_orcid":"https://orcid.org/0009-0007-4426-1869","affiliations":[{"raw_affiliation_string":"Universidade Federal do Par\u00e1","institution_ids":["https://openalex.org/I59606676"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5133582014"],"corresponding_institution_ids":["https://openalex.org/I59606676"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8446999788284302,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8446999788284302,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.037300001829862595,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.02879999950528145,"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/cantor-set","display_name":"Cantor set","score":0.8220000267028809},{"id":"https://openalex.org/keywords/binary-expansion","display_name":"binary expansion","score":0.7620000243186951},{"id":"https://openalex.org/keywords/connected-components","display_name":"connected components","score":0.6309999823570251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8510000109672546},{"id":"https://openalex.org/C36605576","wikidata":"https://www.wikidata.org/wiki/Q273188","display_name":"Cantor set","level":2,"score":0.7996000051498413},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.7208999991416931},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6209999918937683},{"id":"https://openalex.org/C149701218","wikidata":"https://www.wikidata.org/wiki/Q938883","display_name":"Cantor function","level":3,"score":0.53329998254776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5217999815940857},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.48190000653266907},{"id":"https://openalex.org/C55375708","wikidata":"https://www.wikidata.org/wiki/Q1201815","display_name":"Null set","level":3,"score":0.4767000079154968},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4325999915599823},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.42989999055862427},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.39089998602867126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.382099986076355},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3345000147819519},{"id":"https://openalex.org/C70654966","wikidata":"https://www.wikidata.org/wiki/Q729471","display_name":"Cantor's diagonal argument","level":3,"score":0.3292999863624573},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3172000050544739},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3158000111579895},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.3075000047683716},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.302700012922287},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C17327563","wikidata":"https://www.wikidata.org/wiki/Q1991405","display_name":"Nowhere dense set","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23675659","doi":"https://doi.org/10.5281/zenodo.23675659","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23675659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23675660","doi":"https://doi.org/10.5281/zenodo.23675660","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23675660","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23675659","doi":"https://doi.org/10.5281/zenodo.23675659","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23675659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7221776300","https://openalex.org/W272407018","https://openalex.org/W2183564828","https://openalex.org/W3133774523","https://openalex.org/W7033335608","https://openalex.org/W2069952448","https://openalex.org/W7116966752","https://openalex.org/W4405524356","https://openalex.org/W3153786627","https://openalex.org/W1022682125"],"abstract_inverted_index":{"This":[0],"paper":[1,120],"resolves":[2],"the":[3,13,19,36,41,55,62,93,113,141,146,159,162,174],"first":[4],"Jones":[5],"problem":[6],"on":[7],"achievement":[8],"sets.":[9],"We":[10],"prove":[11],"that":[12,104,140],"set":[14,29],"of":[15,18,30,95,132,145,158,176],"all":[16],"subsums":[17],"series":[20],"with":[21,92,112],"terms":[22],"2\u207b\u207f":[23,45],"+":[24,46],"(\u22121)\u207f3\u207b\u207f":[25],"is":[26,82,107],"a":[27,130,167],"Cantor":[28],"positive":[31],"Lebesgue":[32,127],"measure.":[33],"More":[34],"generally,":[35],"same":[37,163],"conclusion":[38],"holds":[39],"for":[40,48,126,134,166],"family":[42],"a\u2099(t)":[43],"=":[44,59],"t(\u22121)\u207f3\u207b\u207f":[47],"every":[49],"nonzero":[50],"real":[51],"parameter":[52],"t,":[53],"whereas":[54],"unperturbed":[56],"case":[57],"t":[58],"0":[60],"gives":[61],"interval":[63,86],"[0,":[64],"1].":[65],"The":[66,119],"proof":[67],"combines":[68],"cylinder":[69],"decompositions,":[70],"tail":[71],"rescaling,":[72],"measure":[73],"estimates,":[74],"and":[75,138,178],"typical":[76],"binary":[77,170],"expansions.":[78],"Its":[79],"central":[80],"argument":[81],"an":[83],"induction":[84],"connecting":[85],"coverings":[87],"by":[88],"finitely":[89],"many":[90],"translates":[91],"multiplicity":[94,106],"representations":[96],"at":[97],"interior":[98],"points.":[99],"An":[100,156],"integral":[101],"identity":[102],"establishes":[103,161],"this":[105,115],"finite":[108,148],"almost":[109],"everywhere;":[110],"together":[111],"induction,":[114],"excludes":[116],"nonempty":[117],"interior.":[118],"also":[121],"provides":[122],"explicit":[123],"lower":[124],"bounds":[125],"measure,":[128],"including":[129],"bound":[131],"1/4":[133],"Jones\u2019s":[135],"original":[136],"set,":[137],"proves":[139],"largest":[142],"connected":[143],"components":[144],"standard":[147],"outer":[149],"approximations":[150],"tend":[151],"to":[152],"zero":[153],"in":[154,173],"length.":[155],"extension":[157],"method":[160],"topological":[164],"classification":[165],"companion":[168],"perturbed":[169],"sequence":[171],"discussed":[172],"survey":[175],"G\u0142\u0105b":[177],"Prus-Wi\u015bniowski.":[179]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-27T00:00:00"}
