{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:26Z","timestamp":1760241806988,"version":"build-2065373602"},"reference-count":3,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T00:00:00Z","timestamp":1534809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present paper we consider one of the basic theorems of probability theory on real numbers. We prove that it is equivalent with the supremum axiom of real numbers.<\/jats:p>","DOI":"10.3390\/axioms7030059","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T11:12:42Z","timestamp":1534849962000},"page":"59","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Alternative to Real Number Axioms"],"prefix":"10.3390","volume":"7","author":[{"given":"Igor","family":"L\u00ed\u0161ka","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, 974 01 Bansk\u00e1 Bystrica, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beloslav","family":"Rie\u010dan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\u00e9ho 40, 974 01 Bansk\u00e1 Bystrica, Slovakia"},{"name":"Institute of Mathematics and Computer Science, Mathematical Institute Slovak Academy of Sciences, \u0160tef\u00e1nikova 49, 814 73 Bratislava, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4432-3528","authenticated-orcid":false,"given":"Anna","family":"Tirp\u00e1kov\u00e1","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Tr. A. Hlinku 1, 949 74 Nitra, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.4169\/amer.math.monthly.120.02.099","article-title":"Toward a More Complete List of Completeness Axiom","volume":"120","author":"Teissman","year":"2013","journal-title":"Am. Math. Mon."},{"key":"ref_2","unstructured":"Rie\u010dan, B., and Neubrunn, T. (2013). Integral, Measure and Ordening, Springer Science & Business Media."},{"key":"ref_3","unstructured":"Billingsley, P. (2008). Probability and Measure, John Wiley & Sons."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/3\/59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:20:12Z","timestamp":1760196012000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/7\/3\/59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,21]]},"references-count":3,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["axioms7030059"],"URL":"https:\/\/doi.org\/10.3390\/axioms7030059","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2018,8,21]]}}}