{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T23:56:27Z","timestamp":1778716587666,"version":"3.51.4"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"8","license":[{"start":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T00:00:00Z","timestamp":1469664000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p>We show that the disintegration operator on a complete separable metric space along a projection map, restricted to measures for which there is a unique continuous disintegration, is strongly Weihrauch equivalent to the limit operator Lim. When a measure does not have a unique continuous disintegration, we may still obtain a disintegration when some basis of continuity sets has the Vitali covering property with respect to the measure; the disintegration, however, may depend on the choice of sets. We show that, when the basis is computable, the resulting disintegration is strongly Weihrauch reducible to Lim, and further exhibit a single distribution realizing this upper bound.<\/jats:p>","DOI":"10.1017\/s0960129516000098","type":"journal-article","created":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T08:35:09Z","timestamp":1469694909000},"page":"1287-1314","source":"Crossref","is-referenced-by-count":7,"title":["On computability and disintegration"],"prefix":"10.1017","volume":"27","author":[{"given":"NATHANAEL L.","family":"ACKERMAN","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CAMERON E.","family":"FREER","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DANIEL M.","family":"ROY","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,7,28]]},"reference":[{"key":"S0960129516000098_ref12","first-page":"301","article-title":"On the definition of probability densities and sufficiency of the likelihood map","volume":"15","author":"Fraser","year":"1995","journal-title":"Probability and Mathematical Statistics"},{"key":"S0960129516000098_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.10.006"},{"key":"S0960129516000098_ref3","first-page":"956","article-title":"Notions of probabilistic computability on represented spaces","volume":"14","author":"Bosserhoff","year":"2008","journal-title":"Journal of Universal Computer Science"},{"key":"S0960129516000098_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2015.03.005"},{"key":"S0960129516000098_ref2","doi-asserted-by":"crossref","unstructured":"Ackerman N.L. , Freer C.E. and Roy D.M. 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