Title
Measure Theory and Fine Properties of Functions (Studies in Advanced Mathematics),Used
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This book provides a detailed examination of the central assertions of measure theory in ndimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine 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 changeofvariable 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.
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- Q: What topics are covered in 'Measure Theory and Fine Properties of Functions'? A: The book covers topics such as abstract measure theory, theorems and differentiation in n-dimensional Euclidean space, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings, and Sobolev functions.
- Q: Who is the author of this book? A: The author of 'Measure Theory and Fine Properties of Functions' is Lawrence C. Evans.
- Q: What is the binding type of this book? A: This book is available in hardcover binding.
- Q: How many pages does this book contain? A: The book contains 280 pages.
- Q: When was 'Measure Theory and Fine Properties of Functions' published? A: The book was published on February 1, 1992.
- Q: Is this book suitable for graduate students? A: Yes, this book is ideal for graduate students in applied mathematics due to its detailed proofs and comprehensive coverage of measure theory.
- Q: What makes this book different from other books on measure theory? A: This book includes complete proofs of key results often omitted in other texts, such as Besicovitch's Covering Theorem and Rademacher's Theorem.
- Q: What is the condition of the book? A: The book is listed as 'New' condition.
- Q: Does this book include practical applications of measure theory? A: Yes, the text emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions, making it useful for applied mathematicians.
- Q: What edition of the book is available? A: This is the first edition of 'Measure Theory and Fine Properties of Functions'.