Geometric properties of disintegration of measures
In this paper we study the connection between disintegration of measures and some geometric properties of probability spaces. We prove a disintegration theorem, and then address disintegration from the perspective of an optimal transport problem. We look at the disintegration of transport plans, whi...
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| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
09-02-2022
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | In this paper we study the connection between disintegration of measures and
some geometric properties of probability spaces. We prove a disintegration
theorem, and then address disintegration from the perspective of an optimal
transport problem. We look at the disintegration of transport plans, which are
used to define and study disintegration maps. Using these objects we study the
regularity and absolute continuity of disintegration of measures. In
particular, we discuss the weak continuity of the disintegration map, we study
some conditions for which one can obtain a path of conditional measures in the
space of probability measures and we show a rigidity condition for the
disintegration of measures to be given into absolutely continuous measures. |
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| DOI: | 10.48550/arxiv.2202.04511 |