{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T23:17:08Z","timestamp":1772234228250,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n\t\t\t\t<jats:p>In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems about the convergence of sequences. We applied definitions introduced in the previous article [21] to the proof of integrability.<\/jats:p>","DOI":"10.2478\/forma-2013-0016","type":"journal-article","created":{"date-parts":[[2014,1,9]],"date-time":"2014-01-09T20:14:15Z","timestamp":1389298455000},"page":"145-152","source":"Crossref","is-referenced-by-count":2,"title":["Riemann Integral of Functions from \u211d into Real Banach Space"],"prefix":"10.2478","volume":"21","author":[{"given":"Keiko","family":"Narita","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","container-title":["Formalized Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/forma\/21\/2\/article-p145.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2013.21.issue-2\/forma-2013-0016\/forma-2013-0016.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T16:17:31Z","timestamp":1590769051000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/forma-2013-0016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.2478\/forma-2013-0016","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2013,6,1]]}}}