Measuring the probabilistic powerdomain
In this paper the authors show that a special class of measurements, called MP-measurements, on a continuous domain extend via a natural construction to measurements on its probabilistic powerdomain. (Here, a measurement is an upper semicontinuous function from a continuous domain, thought of as a ``model'' for the space of its maximal elements equipped with the relative Scott topology, into the non-negative real numbers that (typically) vanishes precisely at the maximal elements.) They show that a number of standard examples of measurements are MP-measurements, and apply their results by giving a new domain-theoretic existence proof of the unique invariant measure for a weighted iterated function system.
scientific article; zbMATH DE number 2110972