Geometric properties of disintegration of measures
Abstract
In this paper, we study a connection between disintegration of measures and geometric properties of probability spaces. We prove a disintegration theorem, addressing 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 exhibit conditions for which the disintegration map is weakly continuous and one can obtain a path of measures given by this map. We show a rigidity condition for the disintegration of measures to be given into absolutely continuous measures.
Keywords
Cite
@article{arxiv.2202.04511,
title = {Geometric properties of disintegration of measures},
author = {Renata Possobon and Christian S. Rodrigues},
journal= {arXiv preprint arXiv:2202.04511},
year = {2025}
}
Comments
34 pages, 5 figures. Accepted in Ergodic Theory and Dynamical Systems. doi:10.1017/etds.2024.74