{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T01:07:49Z","timestamp":1777424869305,"version":"3.51.4"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T00:00:00Z","timestamp":1456790400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-sa\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,3,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p> In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from \u03c3-measure because existence of \u03c3-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals. <\/jats:p>","DOI":"10.1515\/forma-2016-0006","type":"journal-article","created":{"date-parts":[[2016,8,22]],"date-time":"2016-08-22T14:36:23Z","timestamp":1471876583000},"page":"69-79","source":"Crossref","is-referenced-by-count":5,"title":["Product Pre-Measure"],"prefix":"10.1515","volume":"24","author":[{"given":"Noboru","family":"Endou","sequence":"first","affiliation":[{"name":"Gifu National College of Technology Gifu, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2016,8,31]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/24\/1\/article-p69.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2016-0006","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,7]],"date-time":"2021-04-07T00:14:23Z","timestamp":1617754463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2016-0006"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,1]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,8,31]]},"published-print":{"date-parts":[[2016,3,1]]}},"alternative-id":["10.1515\/forma-2016-0006"],"URL":"https:\/\/doi.org\/10.1515\/forma-2016-0006","relation":{},"ISSN":["1898-9934"],"issn-type":[{"value":"1898-9934","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,1]]}}}