{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T08:15:15Z","timestamp":1648541715147},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2015,12,1]],"date-time":"2015-12-01T00:00:00Z","timestamp":1448928000000},"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":[[2015,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a <jats:italic>\u03c3<\/jats:italic>-field and the measure on it. In general, the existence of the measure on <jats:italic>\u03c3<\/jats:italic>-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a <jats:italic>\u03c3<\/jats:italic>-field. Therefore, in this article we define a measure (<jats:monospace>pre-measure<\/jats:monospace>) on a semialgebra and extend it to a measure on a <jats:italic>\u03c3<\/jats:italic>-field. Furthermore, we give a <jats:italic>\u03c3<\/jats:italic>-measure as an extension of the measure on a <jats:italic>\u03c3<\/jats:italic>-field. We follow [24], [10], and [31].<\/jats:p>","DOI":"10.1515\/forma-2015-0025","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T23:40:36Z","timestamp":1459381236000},"page":"309-323","source":"Crossref","is-referenced-by-count":0,"title":["Construction of Measure from Semialgebra of Sets<sup>1<\/sup>"],"prefix":"10.1515","volume":"23","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":[[2016,3,25]]},"container-title":["Formalized Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/23\/4\/article-p309.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2015-0025","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T03:31:14Z","timestamp":1617939074000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/forma-2015-0025"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,1]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,3,25]]},"published-print":{"date-parts":[[2015,12,1]]}},"alternative-id":["10.1515\/forma-2015-0025"],"URL":"https:\/\/doi.org\/10.1515\/forma-2015-0025","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2015,12,1]]}}}