A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Probabilistic non-determinism
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Selected papers of the workshop on Topology and completion in semantics
Handbook of logic in computer science (vol. 3)
Power domains and iterated function systems
Information and Computation
A computational model for metric spaces
Theoretical Computer Science
Domain Theory in Stochastic Processes
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
The Scott Topology Induces the Weak Topology
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Mathematical Structures in Computer Science
The Scott Topology Induces the Weak Topology
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Computability of probability measures and Martin-Löf randomness over metric spaces
Information and Computation
Computable Exchangeable Sequences Have Computable de Finetti Measures
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
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Given a probability measure on a compact metric space, we construct an increasing chain of valuations on the upper space of the metric space whose least upper bound is the measure. We then obtain the expected value of any H\"{o}lder continuous function with respect to the measure up to any precision. We prove that the Scott topology induces the weak topology of the space of probability measures in the following general setting: Whenever a separable metric space is embedded into a subset of the maximal elements of an $\omega$-continuous dcpo, which is a $G_{\delta}$ subset of the dcpo equipped with the Scott topology, we show that the space of probability measures of the metric space equipped with the weak topology is then embedded into a subspace of the maximal elements of the probabilistic power domain of the dcpo. We present a novel application in the theory of periodic doubling route to chaos.