# On computability and disintegration

arXiv: https://arxiv.org/abs/1509.02992 · HTML: https://mlsanity.com/paper/1509.02992/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2015.

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

- [Compositional Semantics for Probabilistic Programs with Exact Conditioning](https://mlsanity.com/paper/2101.11351/) (2021)
- [Minimal Variance Model Aggregation: A principled, non-intrusive, and versatile integration of black box models](https://mlsanity.com/paper/2409.17267/) (2024)

## Abstract (arXiv)

We show that the disintegration operator on a complete separable metric space along a projection map, restricted to measures for which there is a unique continuous disintegration, is strongly Weihrauch equivalent to the limit operator Lim. When a measure does not have a unique continuous disintegration, we may still obtain a disintegration when some basis of continuity sets has the Vitali covering property with respect to the measure; the disintegration, however, may depend on the choice of sets. We show that, when the basis is computable, the resulting disintegration is strongly Weihrauch reducible to Lim, and further exhibit a single distribution realizing this upper bound.