论文标题
措施分解的几何特性
Geometric properties of disintegration of measures
论文作者
论文摘要
在本文中，我们研究了度量分解与概率空间的几何特性之间的联系。我们证明了瓦解定理，从最佳运输问题的角度来解决瓦解。我们查看运输计划的瓦解，这些计划用于定义和研究崩解图。使用这些对象，我们研究了措施分解的规律性和绝对连续性。特别是，我们表现出崩解图弱连续的条件，并且可以获得该地图给出的度量途径。我们显示了将措施分解为绝对连续措施的僵化条件。
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.
