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首页> 美国政府科技报告 >Existence Theorems for Measures on Continuous Posets, with Applications to Random Set Theory.
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Existence Theorems for Measures on Continuous Posets, with Applications to Random Set Theory.

机译：连续集合度量的存在定理及其在随机集理论中的应用。

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We state conditions on a partially ordered set (poset) L and a mapping lambda, defined on a class fancy F sub c of filters on L, under which lambda extends to a measure on the minimal sigma-field over fancy F sub c. By applying this extension result to the case when L is a continuous lattice, all locally finite measures on L are identified as well as all Levy-Khinchin measures. We then characterize these kinds of measures on continuous (inf-) semilattices and continuous posets. An interesting correspondence between Levy-Khinchin measures and inf-infinitely divisible probability measures is presented. The correspondence between probability measures on the line and distribution functions is a particular case of this result. So is also Choquet's characterization of the distributions of all random closed sets in a fixed locally compact second countable Hausdorff space S. Our approach to Choquet's theorem show that it holds as soon as the topology of S is continuous, second countable and sorber. Our method also yields characterizations of the distributions of all random compact and all random compact convex sets in R sub d for finite d. We furthermore obtain characterizations of infinite divisibility under union and sup, resp. for these kinds of random sets. Keywords: Reprints. (kr)

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