arXiv:2202.04511 Abstract | arXiv Analytics

arXiv:2202.04511 [math.PR]Abstract References Reviews Resources

Geometric properties of disintegration of measures

Published 2022-02-09Version 1

In this paper we study the connection of 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. In particular, we look at the disintegration of transport plans, which are used to define and study disintegration maps. Using these objects we study the relationship between disintegration of measures and absolute continuity. We show a condition for disintegration of measures into absolutely continuous measures.

Comments: 26 pages, 4 figures

Categories: math.PR, math.DS

Keywords: geometric properties, study disintegration maps, optimal transport problem, absolute continuity, probability spaces

Related articles: Most relevant | Search more

arXiv:1601.00639 [math.PR] (Published 2016-01-04)

On the equivalence of probability spaces

Daniel Alpay, Palle Jorgensen, David Levanony

arXiv:1905.08739 [math.PR] (Published 2019-05-21)

Absolute continuity of solutions to reaction-diffusion equations with multiplicative noise

Carlo Marinelli, Lluís Quer-Sardanyons

arXiv:math/0606783 [math.PR] (Published 2006-06-30)

On the absolute continuity of Lévy processes with drift