  We construct the space of valuations on a quasi-Polish space in terms of the
characterization of quasi-Polish spaces as spaces of ideals of a countable
transitive relation. Our construction is closely related to domain theoretical
work on the probabilistic powerdomain, and helps illustrate the connections
between domain theory and quasi-Polish spaces. Our approach is consistent with
previous work on computable measures, and can be formalized within weak formal
systems, such as subsystems of second order arithmetic.
