On computability and disintegration

Nathanael L. Ackerman; Cameron E. Freer; Daniel M. Roy

doi:10.1017/s0960129516000098

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arXiv · 1509.02992

On computability and disintegration

Nathanael L. Ackerman·Cameron E. Freer·Daniel M. Roy

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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.

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BibTeX RIS

Nathanael L. Ackerman, Cameron E. Freer, Daniel M. Roy. 2016-05-10. On computability and disintegration. https://doi.org/10.1017/s0960129516000098

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