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Measuring the Probabilistic Powerdomain - Martin, al. (2002) (Correct)
....continuous valuations de ned on the Scott topology D of a dcpo D. The set of all such valuations, ordered by v if and only if (U) U) for all U 2 D, forms a dcpo PD: the probabilistic powerdomain of D. Our main reference for the probabilistic powerdomain is the PhD thesis of Jones [10] from which the following result is taken. Theorem 1 (Jones [10] If D is a continuous domain then PD is continuous with a basis B = f i=1 r i p i j p i 2 Bg; where B D is a basis for D. Proof. Sketch) De ne a dissection of D to be a disjoint family of crescents D = fC i g i2I , where C ....
....dcpo D. The set of all such valuations, ordered by v if and only if (U) U) for all U 2 D, forms a dcpo PD: the probabilistic powerdomain of D. Our main reference for the probabilistic powerdomain is the PhD thesis of Jones [10] from which the following result is taken. Theorem 1 (Jones [10]) If D is a continuous domain then PD is continuous with a basis B = f i=1 r i p i j p i 2 Bg; where B D is a basis for D. Proof. Sketch) De ne a dissection of D to be a disjoint family of crescents D = fC i g i2I , where C i = x i n U i for some x i 2 B and U i 2 D. Given 2 PD and ....
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