منابع مشابه
Continuous valuations
0 Introduction In this paper we study, for a certain type of topological rings A, the topological space Cont A of all equivalence classes of continuous valuations of A. The space ContA is defined as follows. Let v: A-+Fw{0} be a valuation of A, where F is an ordered multiplicative group generated by im(v)\{0}. On Fw [0} we introduce the topology such that U _~ F ~ {0} is open iff 0 q~ U or {xeF...
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Following [Hub93, §3], we introduce the spectrum of continuous valuations Cont(A) for a Huber ring A and the adic spectrum Spa(A,A) for a Huber pair (A,A). We also draw heavily from [Con14; Wed12]. These notes are from the arithmetic geometry learning seminar on adic spaces held at the University of Michigan during the Winter 2017 semester, organized by Bhargav Bhatt. See [Dat17; Ste17] for oth...
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The notion of valuation on convex sets can be considered as a generalization of the notion of measure, which is defined only on the class of convex compact sets. It is well-known that there are important and interesting examples of valuations on convex sets, which are not measures in the usual sense as, for example, the mixed volumes. Basic definitions and some classical examples are discussed ...
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We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel-algebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 1998
ISSN: 1571-0661
DOI: 10.1016/s1571-0661(05)80218-x