This paper is about combining nondeterminism and probabilities. We
study this phenomenon from a domain theoretic point of view.
In domain theory, nondeterminism is modeled using the notion of
powerdomain,
while probability is modeled using the powerdomain of valuations.
Those two functors do not combine well, as they are. We define the
notion of powerdomain of indexed valuations, which can be combined nicely
with the usual nondeterministic powerdomain. We show an equational
characterization of our construction.
Finally we discuss the computational meaning of indexed valuations,
and we show how they can be used, by giving a denotational semantics
of a simple imperative language.
