We continue our previous work  on giving semantics to probabilistic programs using computable distributions. First, we highlight a gap in our previous semantics involving the measurability of an environment lookup function and address it. Second, we suggest topological domains, a category of domains proposed in the literature that supports both Type-2 computability and domain-theoretic constructions, as an alternative to DCPOs in giving semantics to probabilistic programs based on computable distributions.
 D. Huang and G. Morrisett. An Application of Computable Distributions to the Semantics of Probabilistic Programming Languages. In Programming Languages and Systems, pages 337–363. Springer, 2016.