Measure Theory and Fine Properties of Functions

Measure Theory and Fine Properties of Functions
Author :
Publisher : CRC Press
Total Pages : 286
Release :
ISBN-10 : 0849371570
ISBN-13 : 9780849371578
Rating : 4/5 (578 Downloads)

Book Synopsis Measure Theory and Fine Properties of Functions by : Lawrence Craig Evans

Download or read book Measure Theory and Fine Properties of Functions written by Lawrence Craig Evans and published by CRC Press. This book was released on 1991-12-18 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 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.

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"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)