论文信息 - An Extension Result for Continuous Valuations

An Extension Result for Continuous Valuations

Abstract 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 σ-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 result also holds for σ-finite valuations, but fails for dcpo's in general.

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