On computability and disintegration

Abstract

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.

28 pages. Substantially updated following referee suggestions

References in corpus (2)

• Probabilistic Computability and Choice
• How constructive is constructing measures?

Cited by in corpus (6)

• Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints
• Bayesian Probabilistic Numerical Methods
• Paradoxes of Probabilistic Programming
• On the close interaction between algorithmic randomness and constructive/computable measure theory
• Compositional Semantics for Probabilistic Programs with Exact Conditioning
• Point-identification in multivariate nonseparable triangular models