  We give a commutative valuations monad Z on the category DCPO of dcpo's and
Scott-continuous functions. Compared to the commutative valuations monads given
in [Jia et al., 2021], our new monad Z is larger and it contains all
push-forward images of valuations on the unit interval [0,1] along lower
semi-continuous maps. We believe that this new monad will be useful in giving
domain-theoretic denotational semantics for statistical programming languages
with continuous probabilistic choice.
