{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T07:08:48Z","timestamp":1758265728573,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,7,2]],"date-time":"2012-07-02T00:00:00Z","timestamp":1341187200000},"content-version":"vor","delay-in-days":183,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Mathematical Tianyuan Foundation of China","award":["11126087","KJ100518"],"award-info":[{"award-number":["11126087","KJ100518"]}]},{"name":"Chongqing Municipal Educational Committee","award":["11126087","KJ100518"],"award-info":[{"award-number":["11126087","KJ100518"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We prove that for a given normalized compact metric space it can induce a  <jats:italic>\u03c3<\/jats:italic>\u2010max\u2010superdecomposable measure, by constructing a Hausdorff pseudometric on its power set. We also prove that the restriction of this set function to the algebra of all measurable sets is a <jats:italic>\u03c3<\/jats:italic>\u2010max\u2010decomposable  measure. Finally we conclude this paper with two open problems.<\/jats:p>","DOI":"10.1155\/2012\/701206","type":"journal-article","created":{"date-parts":[[2012,7,2]],"date-time":"2012-07-02T21:03:47Z","timestamp":1341263027000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On Decomposable Measures Induced by Metrics"],"prefix":"10.1155","volume":"2012","author":[{"given":"Dong","family":"Qiu","sequence":"first","affiliation":[]},{"given":"Weiquan","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,2]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044450263-6\/50031-2"},{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2434-0"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(87)90354-4"},{"key":"e_1_2_6_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-76852-6"},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081078208934833"},{"key":"e_1_2_6_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90061-1"},{"volume-title":"Theory of Capacities","year":"1953","author":"Choquet G.","key":"e_1_2_6_7_2"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/0470013850"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488502001831"},{"key":"e_1_2_6_10_2","first-page":"89","article-title":"Applications of decomposable measures on nonlinear difference equations","volume":"31","author":"Pap E.","year":"2001","journal-title":"Novi Sad Journal of Mathematics"},{"volume-title":"Fractals Everywhere","year":"1988","author":"Barnsley M.","key":"e_1_2_6_11_2"},{"key":"e_1_2_6_12_2","first-page":"479","article-title":"The Hausdorff nearest circle to a convex compact set in the plane","volume":"17","author":"Ginchev I.","year":"1998","journal-title":"Journal for Analysis and Its Applications"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.02.014"},{"key":"e_1_2_6_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8149-3"},{"volume-title":"Linear Operators, General Theory (Part 1)","year":"1988","author":"Dunford N.","key":"e_1_2_6_15_2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/701206.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/701206.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/701206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:09:10Z","timestamp":1718089750000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/701206"}},"subtitle":[],"editor":[{"given":"C.","family":"Conca","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/701206"],"URL":"https:\/\/doi.org\/10.1155\/2012\/701206","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2012-04-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-06-09","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-07-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"701206"}}