Analysis on Polish Spaces and an Introduction to Optimal Transportation
Analysis on Polish Spaces and an Introduction to Optimal Transportation
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波兰空间分析和最优运输简介
DOI：
10.1017/9781108377362
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发表时间：
2017
期刊：
影响因子：
1.7
通讯作者：
D. Garling
中科院分区：
文献类型：
--
作者：
D. Garling
数学分析（包括纯数学分析和应用数学分析）的很大一部分内容是在波兰空间上进行的：波兰空间是一种拓扑空间，其拓扑可由一个完备度量给出。这种分析不仅比一般情况下更简单，而且更关键的是，它包含许多重要的特殊结果。本书详细阐述了波兰空间上的分析和测度理论，包括关于概率测度空间的结果。书中包含200多个基础练习题，对于高等数学专业的学生以及数学分析领域的研究人员来说，它将是一个有用的资源。本书还包括对最优运输理论的一个简单易懂的介绍，说明了本书前面所确立的许多结果在该理论中起着至关重要的作用。
A large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces of probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in mathematical analysis. The book also includes a straightforward and gentle introduction to the theory of optimal transportation, illustrating just how many of the results established earlier in the book play an essential role in the theory.