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We identify the class of general probabilistic theories which also admit Gleason-type theorems. It contains theories satisfying the no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.<\/jats:p>","DOI":"10.22331\/q-2021-11-25-588","type":"journal-article","created":{"date-parts":[[2021,11,25]],"date-time":"2021-11-25T13:48:29Z","timestamp":1637848109000},"page":"588","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["General Probabilistic Theories with a Gleason-type Theorem"],"prefix":"10.22331","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3523-7553","authenticated-orcid":false,"given":"Victoria J","family":"Wright","sequence":"first","affiliation":[{"name":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, 80-308 Gda\u0144sk, Poland"},{"name":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6647-3252","authenticated-orcid":false,"given":"Stefan","family":"Weigert","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of York, York YO10 5DD, United Kingdom"}]}],"member":"9598","published-online":{"date-parts":[[2021,11,25]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"George W Mackey. 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