{"id":"https://openalex.org/W2169450769","doi":"https://doi.org/10.1112/jlms/jdu031","title":"Exact dimensionality and projections of random self-similar measures and sets","display_name":"Exact dimensionality and projections of random self-similar measures and sets","publication_year":2014,"publication_date":"2014-07-14","ids":{"openalex":"https://openalex.org/W2169450769","doi":"https://doi.org/10.1112/jlms/jdu031","mag":"2169450769"},"language":"en","primary_location":{"id":"doi:10.1112/jlms/jdu031","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu031","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/1212.1345","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kenneth J. Falconer","orcid":null},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Kenneth J. Falconer","raw_affiliation_strings":["School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, KY16 9SS, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, KY16 9SS, United Kingdom","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"last","author":{"id":null,"display_name":"Xiong Jin","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Xiong Jin","raw_affiliation_strings":["School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom, [email protected]"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom, [email protected]","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I16835326"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":5.8228,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.9694393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"90","issue":"2","first_page":"388","last_page":"412"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9628000259399414,"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":0.9628000259399414,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.006000000052154064,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.004000000189989805,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6297000050544739},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5120999813079834},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4860999882221222},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.44119998812675476},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.42879998683929443},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.40299999713897705},{"id":"https://openalex.org/keywords/random-compact-set","display_name":"Random compact set","score":0.3718000054359436},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.3601999878883362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6783000230789185},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5120999813079834},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4860999882221222},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.44119998812675476},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.42879998683929443},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3831999897956848},{"id":"https://openalex.org/C52627884","wikidata":"https://www.wikidata.org/wiki/Q4424101","display_name":"Random compact set","level":4,"score":0.3718000054359436},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3614000082015991},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C205301714","wikidata":"https://www.wikidata.org/wiki/Q228249","display_name":"Random measure","level":3,"score":0.3319000005722046},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.325300008058548},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30320000648498535},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C2639959","wikidata":"https://www.wikidata.org/wiki/Q1344778","display_name":"Distance measures","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.257099986076355},{"id":"https://openalex.org/C13929819","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Random function","level":3,"score":0.2542000114917755}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1112/jlms/jdu031","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdu031","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:1212.1345","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.1345","pdf_url":"https://arxiv.org/pdf/1212.1345","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:pure.atira.dk:openaire_cris_publications/190884fd-96ee-41ca-b372-68b2125355d3","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/190884fd-96ee-41ca-b372-68b2125355d3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Falconer, K J & Jin, X 2014, 'Exact dimensionality and projections of random self-similar measures and sets', J. Lond. Math. Soc. (2), vol. 90, no. 2, pp. 388-412. https://doi.org/10.1112/jlms/jdu031","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.atira.dk:publications/190884fd-96ee-41ca-b372-68b2125355d3","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/exact-dimensionality-and-projections-of-random-selfsimilar-measures-and-sets(190884fd-96ee-41ca-b372-68b2125355d3).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Falconer, K J & Jin, X 2014, 'Exact dimensionality and projections of random self-similar measures and sets', J. Lond. Math. Soc. (2), vol. 90, no. 2, pp. 388-412. https://doi.org/10.1112/jlms/jdu031","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-repository.st-andrews.ac.uk:10023/5514","is_oa":false,"landing_page_url":"https://hdl.handle.net/10023/5514","pdf_url":null,"source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"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":"Journal article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1212.1345","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.1345","pdf_url":"https://arxiv.org/pdf/1212.1345","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":25,"referenced_works":["https://openalex.org/W182240522","https://openalex.org/W1964486846","https://openalex.org/W1969918066","https://openalex.org/W1976186789","https://openalex.org/W1977646629","https://openalex.org/W1983464946","https://openalex.org/W1997287185","https://openalex.org/W2022779339","https://openalex.org/W2025940417","https://openalex.org/W2029275558","https://openalex.org/W2049628118","https://openalex.org/W2070835763","https://openalex.org/W2073997685","https://openalex.org/W2086757836","https://openalex.org/W2109208637","https://openalex.org/W2112797376","https://openalex.org/W2115798948","https://openalex.org/W2120045167","https://openalex.org/W2149123301","https://openalex.org/W2332552440","https://openalex.org/W2962852664","https://openalex.org/W4231110773","https://openalex.org/W4240810995","https://openalex.org/W4249775755","https://openalex.org/W7047028572"],"related_works":[],"abstract_inverted_index":{"We":[0,14,74],"study":[1],"the":[2,71],"geometric":[3],"properties":[4],"of":[5,32,57],"random":[6,63],"multiplicative":[7],"cascade":[8],"measures":[9,18,60,64],"defined":[10],"on":[11,55,70,86],"self-similar":[12,37,59,78],"sets.":[13,73,93],"show":[15],"that":[16],"such":[17],"and":[19,22,34,52,80,91],"their":[20],"projections":[21,56],"sections":[23],"are":[24],"almost":[25],"surely":[26],"exact":[27],"dimensional,":[28],"generalizing":[29],"a":[30,42],"result":[31],"Feng":[33],"Hu":[35],"for":[36],"measures.":[38],"This,":[39],"together":[40],"with":[41],"compact":[43],"group":[44],"extension":[45],"argument,":[46],"enables":[47],"us":[48],"to":[49,61,77],"generalize":[50],"Hochman":[51],"Shmerkin's":[53],"theorems":[54],"deterministic":[58],"these":[62],"without":[65],"requiring":[66],"any":[67],"separation":[68],"conditions":[69],"underlying":[72],"give":[75],"applications":[76],"sets":[79],"fractal":[81],"percolation,":[82],"including":[83],"new":[84],"results":[85],"projections,":[87],"C":[88],"1":[89],"-images":[90],"distance":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2016-06-24T00:00:00"}