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Measure Theory and Fine Properties of Functions, Revised Edition - Lawrence Craig Evans

Measure Theory and Fine Properties of Functions, Revised Edition

Buch | Hardcover
314 Seiten
2015
Chapman & Hall/CRC (Verlag)
978-1-4822-4238-6 (ISBN)
CHF 139,60 inkl. MwSt
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This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. It emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. The book covers theorems
Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.

Topics covered include a quick review of abstract measure theory, theorems and differentiation in ℝn, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as 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), area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrov's theorem (on the twice differentiability a.e. of convex functions).

This revised edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the π-λ theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated.

Topics are carefully selected and the proofs are succinct, but complete. This book provides ideal reading for mathematicians and graduate students in pure and applied mathematics.

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

General Measure Theory. Hausdorff Measures. Area and Coarea Formulas. Sobolev Functions. Functions of Bounded Variation, Sets of Finite Perimeter. Differentiability, Approximation by C1 Functions. Bibliography.

Reihe/Serie Textbooks in Mathematics
Zusatzinfo 15 Illustrations, black and white
Sprache englisch
Maße 156 x 234 mm
Gewicht 480 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
ISBN-10 1-4822-4238-9 / 1482242389
ISBN-13 978-1-4822-4238-6 / 9781482242386
Zustand Neuware
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