Measure Theory and Fine Properties of Functions (Studies in Advance Mathematics) pdf epub mobi txt 电子书 下载 2025
- 测度论
- 数学
- 几何测度论
- 使劲嚼
- Mathematics
- 几何
- measure
- PDE
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the find properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions).Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
具体描述
读后感
评分
评分
评分
评分
用户评价
这本书的特点和书名非常契合，就是FINE(精细)。前面的每一条大定理都是为后面作铺垫。Area/Coarea公式的确是全书的最高潮，尽管定理的证明叙述有些啰嗦与凌乱，但仔细琢磨，真是觉得证明赏心悦目。正所谓“而世之奇伟瑰怪非常之观，常在于险远。”（当然，要有一个讲课水平很高的人来带就更好了。不然可能会迷失在细节中）
评分包含了实分析中的基本内容
评分这本书是一本典型的几何测度论方向的工具书，包括了测度论，Area formula, Sobolev与BV空间等方面的基本知识。作者基本上是在罗列证明，而并未有太多关于证明思路的阐述。本书适合于研究者参考，而不建议初学者学习使用。
评分包含了实分析中的基本内容
评分这本书是一本典型的几何测度论方向的工具书，包括了测度论，Area formula, Sobolev与BV空间等方面的基本知识。作者基本上是在罗列证明，而并未有太多关于证明思路的阐述。本书适合于研究者参考，而不建议初学者学习使用。
相关图书
本站所有内容均为互联网搜索引擎提供的公开搜索信息，本站不存储任何数据与内容，任何内容与数据均与本站无关，如有需要请联系相关搜索引擎包括但不限于百度，google,bing,sogou 等
© 2025 book.wenda123.org All Rights Reserved. 图书目录大全 版权所有