发表于2024-12-23
Measure Theory and Fine Properties of Functions (Studies in Advance Mathematics) 2024 pdf epub mobi 电子书
图书标签: 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.
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。
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
Measure Theory and Fine Properties of Functions (Studies in Advance Mathematics) 2024 pdf epub mobi 电子书