# Measurable Cones and Stable, Measurable Functions

arXiv: https://arxiv.org/abs/1711.09640 · HTML: https://mlsanity.com/paper/1711.09640/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2017.

## Built on by (most cited first, 2 of 2)

- [ωPAP Spaces: Reasoning Denotationally About Higher-Order, Recursive Probabilistic and Differentiable Programs](https://mlsanity.com/paper/2302.10636/) (2023)
- [Nonparametric Involutive Markov Chain Monte Carlo](https://mlsanity.com/paper/2211.01100/) (2022)

## Abstract (arXiv)

We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the main primitives of probabilistic functional programming, like continuous and discrete probabilistic distributions, sampling, conditioning and full recursion. We prove the soundness and adequacy of this model with respect to a call-by-name operational semantics and give some examples of its denotations.