Geometric properties of disintegration of measures

Author(s)

Possobon, Renata ; Rodrigues, Christian S.

• Document type: Journal article
• Source: Ergodic Theory and Dynamical Systems; v. N/A, p. 30-pg., 2024-10-11.

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. (AU)

• FAPESP's process: 18/05309-3 - Geometric and statistical properties of dynamical systems via optimal transport theory
• Grantee: Renata Possobon
• Support Opportunities: Scholarships in Brazil - Master
• FAPESP's process: 20/04426-6 - Stochastic dynamics: analytical and geometrical aspects with applications
• Grantee: Paulo Regis Caron Ruffino
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 19/14724-7 - Geometric and statistical properties of dynamical systems: disintegration of measures
• Grantee: Renata Possobon
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• FAPESP's process: 16/00332-1 - Geometry and probability in dynamical systems: fundamentals and applications
• Grantee: Christian da Silva Rodrigues
• Support Opportunities: Research Grants - Young Investigators Grants