{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T15:30:31Z","timestamp":1762270231373},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[1997,10,1]],"date-time":"1997-10-01T00:00:00Z","timestamp":875664000000},"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":[[1997,10]]},"abstract":"<jats:p>We construct an approximating chain of simple valuations on \nthe upper space of a compact \nmetric space whose lub is a given probability measure on the metric space. \nWe show that \nwhenever a separable metric space is homeomorphic to a <jats:italic>G<\/jats:italic><jats:sub>\u03b4<\/jats:sub> \nsubset of an \u03c9-continuous \ndcpo equipped with its Scott topology, the space of probability measures \nof the metric space \nequipped with the weak topology is homeomorphic with a subset of the maximal\n elements \nof the probabilistic power domain of the \u03c9-continuous dcpo. Given\n an effective \napproximation of a probability measure by an increasing chain of \nnormalised valuations on \nthe upper space of a compact metric space, we show that the \nexpected value of any H\u00f6lder \ncontinuous function on the space can be obtained up to any given \naccuracy. We present a \nnovel application in computing integrals in dynamical systems. We obtain \nan algorithm to \ncompute the expected value of any H\u00f6lder continuous function with \nrespect to the unique \ninvariant measure of the Feigenbaum map in the periodic doubling route\n to chaos.<\/jats:p>","DOI":"10.1017\/s0960129597002338","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:29:40Z","timestamp":1027776580000},"page":"401-417","source":"Crossref","is-referenced-by-count":34,"title":["When Scott is weak on the top"],"prefix":"10.1017","volume":"7","author":[{"given":"ABBAS","family":"EDALAT","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[1997,10,1]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129597002338","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T20:12:44Z","timestamp":1557605564000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129597002338\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,10]]},"references-count":0,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1997,10]]}},"alternative-id":["S0960129597002338"],"URL":"https:\/\/doi.org\/10.1017\/s0960129597002338","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,10]]}}}