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An extension result for continuous valuations

✍ Scribed by M. Alvarez-Manilla; A. Edalat; N. Saheb-Djahromi

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
773 KB
Volume
13
Category
Article
ISSN
1571-0661

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✦ Synopsis

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 c o n tinuous domain can be extended uniquely to a Borel measure. The result also holds for -nite valuations, but fails for dcpo's in general.

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