{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:43:53Z","timestamp":1770756233634,"version":"3.50.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T00:00:00Z","timestamp":1503964800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T00:00:00Z","timestamp":1503964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T00:00:00Z","timestamp":1503964800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["320571"],"award-info":[{"award-number":["320571"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a mathematically well-behaved total function. The output of this `hyper' normalisation operation is a distribution of distributions. It improves reasoning about normalisation.   After developing the basics of this theory of (hyper) normalisation, it is put to use in a similarly new description of conditioning, producing a distribution of conditional distributions. This is used to give a clean abstract reformulation of refinement in quantitative information flow.<\/jats:p>","DOI":"10.23638\/lmcs-13(3:17)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:30Z","timestamp":1743701310000},"source":"Crossref","is-referenced-by-count":2,"title":["Hyper Normalisation and Conditioning for Discrete Probability Distributions"],"prefix":"10.23638","volume":"Volume 13, Issue 3","author":[{"given":"Bart","family":"Jacobs","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,8,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1607.02790v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1607.02790v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:30Z","timestamp":1743701310000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(3:17)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1607.02790v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1607.02790v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1607.02790v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1607.02790","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1607.02790","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,29]]},"article-number":"2009"}}