Measure Theory and Fine Properties of Functions (Studies in Advanced Mathematics)

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9780849371578: Measure Theory and Fine Properties of Functions (Studies in Advanced Mathematics)

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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About the Author:

Lawrence Craig Evans, University of California, Berkeley, USA
Ronald F. Gariepy, University of Kentucky, Lexington, USA

Review:

"This is a new revised edition of a very successful book dealing with measure theory in Rn and some special properties of functions, usually omitted from books dealing with abstract measure theory, but which a working mathematician analyst must know. ... The book is clearly written with complete proofs, including all technicalities. ... The new edition benefits from LaTeX retyping, yielding better cross-references, as well as numerous improvements in notation, format, and clarity of exposition. The bibliography has been updated and several new sections were added ... this welcome, updated, and revised edition of a very popular book will continue to be of great interest for the community of mathematicians interested in mathematical analysis in Rn."
Studia Universitatis Babes-Bolyai Mathematica, 60, 2015

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