{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T11:24:39Z","timestamp":1648725879726},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":2967,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2005,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is shown to be consistent with set theory that every set of reals of size \u2135<jats:sub>1<\/jats:sub> is null yet there are \u2135<jats:sub>1<\/jats:sub> planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.<\/jats:p>","DOI":"10.2178\/bsl\/1130335207","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:50:27Z","timestamp":1197557427000},"page":"517-525","source":"Crossref","is-referenced-by-count":0,"title":["Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle"],"prefix":"10.1017","volume":"11","author":[{"given":"Juris","family":"Stepr\u0101ns","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600002973_ref014","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1970-0265411-1"},{"key":"S1079898600002973_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02792533"},{"key":"S1079898600002973_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02801467"},{"key":"S1079898600002973_ref019","first-page":"225","article-title":"Sur la mesure de la projection d'un compact et certaines familles de cercles","volume":"104","author":"Talagrand","year":"1980","journal-title":"Bulletin des Sciences Math\u00e9matiques, (2)"},{"key":"S1079898600002973_ref013","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1968-0224606-4"},{"key":"S1079898600002973_ref008","first-page":"335","volume":"9","author":"Jackson","year":"2003","journal-title":"Survey of the Steinhaus tiling problem"},{"key":"S1079898600002973_ref015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1974-13343-4"},{"key":"S1079898600002973_ref007","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.222551699"},{"key":"S1079898600002973_ref017","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-99-02197-2"},{"key":"S1079898600002973_ref018","doi-asserted-by":"publisher","DOI":"10.2307\/2586494"},{"key":"S1079898600002973_ref012","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300009748"},{"key":"S1079898600002973_ref010","doi-asserted-by":"crossref","first-page":"143","DOI":"10.4064\/fm-164-2-143-163","article-title":"Convexity ranks in higher dimensions","volume":"164","author":"Kojman","year":"2000","journal-title":"Fundamenta Mathematicae"},{"key":"S1079898600002973_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF02802497"},{"key":"S1079898600002973_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2044851"},{"key":"S1079898600002973_ref016","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.73.7.2174"},{"key":"S1079898600002973_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02785863"},{"key":"S1079898600002973_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-02-00400-9"},{"key":"S1079898600002973_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-02-06437-7"},{"key":"S1079898600002973_ref003","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100056681"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600002973","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T19:34:13Z","timestamp":1556912053000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600002973\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,12]]}},"alternative-id":["S1079898600002973"],"URL":"https:\/\/doi.org\/10.2178\/bsl\/1130335207","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,12]]}}}