{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T10:26:13Z","timestamp":1648635973081},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n\t\t\t\t<jats:p>We have been working on the formalization of the probability and the randomness. In [15] and [16], we formalized some theorems concerning the real-valued random variables and the product of two probability spaces. In this article, we present the generalized formalization of [15] and [16]. First, we formalize the random variables of arbitrary set and prove the equivalence between random variable on \u03a3, Borel sets and a real-valued random variable on \u03a3. Next, we formalize the product of countably infinite probability spaces.<\/jats:p>","DOI":"10.2478\/forma-2013-0003","type":"journal-article","created":{"date-parts":[[2013,8,27]],"date-time":"2013-08-27T20:05:45Z","timestamp":1377633945000},"page":"33-39","source":"Crossref","is-referenced-by-count":0,"title":["Random Variables and Product of Probability Spaces"],"prefix":"10.2478","volume":"21","author":[{"given":"Hiroyuki","family":"Okazaki","sequence":"first","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\/1\/article-p33.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/forma.2013.21.issue-1\/forma-2013-0003\/forma-2013-0003.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T16:17:26Z","timestamp":1590769046000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/forma-2013-0003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":0,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.2478\/forma-2013-0003","relation":{},"ISSN":["1898-9934","1426-2630"],"issn-type":[{"value":"1898-9934","type":"electronic"},{"value":"1426-2630","type":"print"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}