{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T15:47:13Z","timestamp":1770565633736,"version":"3.49.0"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,2]],"date-time":"2018-03-02T00:00:00Z","timestamp":1519948800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"DGI-PUCP","award":["441"],"award-info":[{"award-number":["441"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We derive the Born probability rule from Gudder\u2019s theorem\u2014a theorem that addresses orthogonally-additive functions. These functions are shown to be tightly connected to the functions that enter the definition of a signed measure. By imposing some additional requirements besides orthogonal additivity, the addressed functions are proved to be linear, so they can be given in terms of an inner product. By further restricting them to act on projectors, Gudder\u2019s functions are proved to act as probability measures obeying Born\u2019s rule. The procedure does not invoke any property that fully lies within the quantum framework, so Born\u2019s rule is shown to apply within both the classical and the quantum domains.<\/jats:p>","DOI":"10.3390\/e20030158","type":"journal-article","created":{"date-parts":[[2018,3,2]],"date-time":"2018-03-02T11:53:40Z","timestamp":1519991620000},"page":"158","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Gudder\u2019s Theorem and the Born Rule"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3757-1769","authenticated-orcid":false,"given":"Francisco","family":"De Zela","sequence":"first","affiliation":[{"name":"Departamento de Ciencias, Secci\u00f3n F\u00edsica, Pontificia Universidad Cat\u00f3lica del Per\u00fa, Apartado 1761, Lima, Peru"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,2]]},"reference":[{"key":"ref_1","first-page":"885","article-title":"Measures on the closed subspaces of a Hilbert space","volume":"6","author":"Gleason","year":"1957","journal-title":"J. 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