離散型的Brunn Minkowski不等式綜覽

Abstract

在本論文中，我們會先定義一個Brunn-Minkowski不等式。然後我們在第一部 分中首先證明它會收斂。在第二部分中，我們會證明一個離散型式的metric space 也會滿足Brunn-Minkowski不等式。

In the rst part of the paper, we give a new de nition of Brunn- Minkowski inequality in metric measure space. Then we show the stability of Brunn-Minkowski inequality under a convergence of metric measure space. This result gives as a corollary the stability of the classical Brunn- Minkowski inequality for geodesic spaces. In the second part, we show that every metric measure space satisfying Brunn-Minkowski inequality can be approximated by discrete space with some approximated Brunn-Minkowski inequalities.