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We study probability measures on the set of natural extensions of a causal set, especially those measures having the property of<jats:italic>order-invariance<\/jats:italic>: if we condition on the set of the bottom<jats:italic>k<\/jats:italic>elements of the natural extension, each feasible ordering among these<jats:italic>k<\/jats:italic>elements is equally likely. We give sufficient conditions for the existence and uniqueness of an order-invariant measure on the set of natural extensions of a causal set.<\/jats:p>","DOI":"10.1017\/s0963548311000721","type":"journal-article","created":{"date-parts":[[2012,1,19]],"date-time":"2012-01-19T13:32:20Z","timestamp":1326979940000},"page":"330-357","source":"Crossref","is-referenced-by-count":6,"title":["Order-Invariant Measures on Fixed Causal Sets"],"prefix":"10.1017","volume":"21","author":[{"given":"GRAHAM","family":"BRIGHTWELL","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MALWINA","family":"LUCZAK","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,1,19]]},"reference":[{"key":"S0963548311000721_ref18","first-page":"527","article-title":"Asymptotics of the Plancherel measure of the symmetric group and the limiting shape of Young tableaux","volume":"18","author":"Vershik","year":"1977","journal-title":"Soviet Math. 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