Roughly, the following works prefers unnormalized kernels over substochastic kernels.
- Commutative Semantics for Probabilistic Programming (Staton, 2017) uses unnormalized kernels from the abstract.
- Semantics of Probabilistic Programs (Kozen, 1981) uses cones, like positive subsets of powers of the reals.
- Contextual Equivalence for Probabilistic Programs with Continuous Random Variables and Scoring (Culpepper, Cobb) explicitly argues against subdistributions.
- An Introduction to Probabilistic Programming (van de Meent, Paige, Yang, Wood, 2021)
- Measurable Cones and Stable, Measurable Functions (Ehrhard, Pagani, Tasson, 2017)
The following is literature that prefers substochastic kernels over unnormalized kernels.
- The Category of Markov Kernels (Panangaden, 1999), substochastic Giry monad.
- Labelled Markov Processes (Panangaden), substochastic Giry monad.
- A Lambda-Calculus Foundation for Universal Probabilistic Programming (Borgstrom, Dal Lago, et al)
- Lambda Calculus and Probabilistic Computation (Faggian, Ronchi della Rocca, 2019)
- Partial Markov Categories (Di Lavore, Roman, Sobocinski, 2025), subprobability Kleisli categories.