{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T00:14:43Z","timestamp":1777421683449,"version":"3.51.4"},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,1,1]]},"DOI":"10.2478\/v10037-008-0044-9","type":"journal-article","created":{"date-parts":[[2009,3,21]],"date-time":"2009-03-21T01:07:25Z","timestamp":1237597645000},"source":"Crossref","is-referenced-by-count":2,"title":["On L1 Space Formed by Real-Valued Partial Functions"],"prefix":"10.2478","volume":"16","author":[{"given":"Yasushige","family":"Watase","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noboru","family":"Endou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasunari","family":"Shidama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","reference":[{"key":"1","first-page":"565","article-title":"Ring ideals","volume":"3","author":"Jonathan Backer","year":"2001","journal-title":"Formalized Mathematics"},{"key":"2","first-page":"485","article-title":"Miscellaneous facts about functions","volume":"4","author":"Grzegorz Bancerek","year":"1996","journal-title":"Formalized Mathematics"},{"key":"3","first-page":"433","article-title":"Group and field definitions","volume":"3","author":"J\u00f3zef Bia\u0142as.","year":"1990","journal-title":"Formalized Mathematics"},{"key":"4","first-page":"163","article-title":"Infimum and supremum of the set of real numbers. Measure theory","volume":"1","author":"J\u00f3zef Bia\u0142as.","year":"1991","journal-title":"Formalized Mathematics"},{"key":"5","first-page":"173","article-title":"Series of positive real numbers. Measure theory","volume":"1","author":"J\u00f3zef Bia\u0142as.","year":"1991","journal-title":"Formalized Mathematics"},{"key":"6","first-page":"263","article-title":"The \u03c3-additive measure theory","volume":"2","author":"J\u00f3zef Bia\u0142as.","year":"1991","journal-title":"Formalized Mathematics"},{"key":"7","first-page":"175","article-title":"Binary operations","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"8","first-page":"55","article-title":"Functions and their basic properties","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"9","first-page":"153","article-title":"Functions from a set to a set","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"10","first-page":"357","article-title":"Partial functions","volume":"2","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"11","first-page":"47","article-title":"Some basic properties of sets","volume":"1","author":"Czes\u0142aw Byli\u0144ski","year":"1990","journal-title":"Formalized Mathematics"},{"key":"12","first-page":"53","article-title":"Integral of measurable function","volume":"2","author":"Noboru Endou","year":"2006","journal-title":"Formalized Mathematics"},{"key":"13","first-page":"35","article-title":"Basic properties of real numbers","volume":"1","author":"Krzysztof Hryniewiecki","year":"1990","journal-title":"Formalized Mathematics"},{"key":"14","first-page":"279","article-title":"Properties of partial functions from a domain to the set of real numbers","volume":"2","author":"Jaros\u0142aw Kotowicz","year":"1992","journal-title":"Formalized Mathematics"},{"key":"15","first-page":"401","article-title":"\u03c3-fields and probability","volume":"2","author":"Andrzej Nedzusiak","year":"1990","journal-title":"Formalized Mathematics"},{"key":"16","first-page":"555","article-title":"Real functions spaces","volume":"3","author":"Henryk Oryszczyszyn","year":"1990","journal-title":"Formalized Mathematics"},{"key":"17","first-page":"147","article-title":"Families of sets","volume":"1","author":"Beata Padlewska","year":"1990","journal-title":"Formalized Mathematics"},{"key":"18","first-page":"111","article-title":"Real normed space","volume":"1","author":"Jan Popio\u0142ek.","year":"1991","journal-title":"Formalized Mathematics"},{"key":"19","first-page":"143","article-title":"Integral of real-valued measurable function.","volume":"4","author":"Yasunari Shidama","year":"2006","journal-title":"Formalized Mathematics"},{"key":"20","first-page":"329","article-title":"Binary operations applied to functions","volume":"2","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"21","first-page":"115","article-title":"Domains and their Cartesian products","volume":"1","author":"Andrzej Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"22","first-page":"297","article-title":"Trybulec. Subspaces and cosets of subspaces in real linear space","volume":"2","author":"A. Wojciech","year":"1990","journal-title":"Formalized Mathematics"},{"key":"23","first-page":"291","article-title":"Trybulec. Vectors in real linear space","volume":"2","author":"A. Wojciech","year":"1990","journal-title":"Formalized Mathematics"},{"key":"24","first-page":"67","article-title":"Properties of subsets","volume":"1","author":"Zinaida Trybulec","year":"1990","journal-title":"Formalized Mathematics"},{"key":"25","first-page":"181","article-title":"Relations defined on sets","volume":"1","author":"Edmund Woronowicz","year":"1990","journal-title":"Formalized Mathematics"}],"container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2008.16.issue-4\/v10037-008-0044-9\/v10037-008-0044-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,30]],"date-time":"2020-05-30T15:27:34Z","timestamp":1590852454000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10037-008-0044-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,1]]},"references-count":25,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.2478\/v10037-008-0044-9","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2008,1,1]]}}}