指導教授：王藹農臺灣大學：數學研究所施柏丞Shih, Po-ChenPo-ChenShih2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264003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.口試委員會審定書……………………………………………………………… i 中文摘要………………………………………………………………………… ii 1. Introduction………………………………………………………………….. 1 2. Stability of Brunn-Minkowski inequality………..............………………….. 2 3. Discretization of metric space.............................................................. 6 參考文獻…………………………………………………………………….…… 8467941 bytesapplication/pdf論文公開時間：2014/07/08論文使用權限：同意有償授權(權利金給回饋學校)Brunn-Minkowski 不等式thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264003/1/ntu-103-R99221029-1.pdf