Abstract

Introduction We show that the probabilistic powerdomain of a Lawson-compact continuous domain is again Lawson-compact. The proof is a fairly straightforward but slightly delicate calculation with so-called simple valuations. A more conceptual proof, using one of the many characterizations of Lawson-compactness, would be preferable. What we are really looking for is a similar result for FS-domains. Lawsoncompactness amounts to only "two-thirds" of this (see Theorem 6 in Chapter 8 of [Plo81]); the remaining third seems very hard to achieve, even for very simple posets, cf. the discussion in [Tix95]. 2 Background We assume familiarity with the theory of continuous domains as laid out in [AJ94] or [Law88]. Our proof will be based on the following criterion for Lawsoncompactness from [Jun89]: Lemma 1 A continuous domain D with bottom element is Lawson-compact, if and only if for every situation x ø x 0

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