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Synopsis
This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space, with emphasis upon the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.
Measure Theory and Fine Properties of Functions, Second Edition includes many interesting items working mathematical analysts need to know, but are rarely taught. Topics covered include a review of abstract measure theory, including Besicovitch’s covering theorem, Rademacher’s theorem (on the differentiability a.e. of Lipschitz continuous functions), the 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).
The 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. The authors assume readers are at least fairly conversant with both Lebesgue measure and abstract measure theory, and the expository style reflects this expectation. The book does not offer lengthy heuristics or motivation, but as compensation presents all the technicalities of the proofs.
This new Second Edition has been updated to provide corrections and minor edits from the previous Revised Edition, with countless improvements in notation, format and clarity of exposition. Also new is a section on the sub differentials of convex functions, and in addition the bibliography has been updated.
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About the Author
Lawrence C. Evans, University of California, Berkeley, USA
Ronald F. Gariepy, University of Kentucky, Lexington, USA
"About this title" may belong to another edition of this title.
- PublisherChapman and Hall/CRC
- Publication date2025
- ISBN 10 103294644X
- ISBN 13 9781032946443
- BindingHardcover
- LanguageEnglish
- Edition number2
- Number of pages340
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Measure Theory and Fine Properties of Functions
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Measure Theory and Fine Properties of Functions
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Measure Theory and Fine Properties of Functions, Revised Edition
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Measure Theory and Fine Properties of Functions
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Measure Theory and Fine Properties of Functions (Hardcover)
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Hardcover. Condition: new. Hardcover. This popular textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space, with emphasis upon the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions.Measure Theory and Fine Properties of Functions, Second Edition includes many interesting items working mathematical analysts need to know, but are rarely taught. Topics covered include a review of abstract measure theory, including Besicovitchs covering theorem, Rademachers theorem (on the differentiability a.e. of Lipschitz continuous functions), the area and coarea formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Aleksandrovs theorem (on the twice differentiability a.e. of convex functions).The 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. The authors assume readers are at least fairly conversant with both Lebesgue measure and abstract measure theory, and the expository style reflects this expectation. The book does not offer lengthy heuristics or motivation, but as compensation presents all the technicalities of the proofs.This new Second Edition has been updated to provide corrections and minor edits from the previous Revised Edition, with countless improvements in notation, format and clarity of exposition. Also new is a section on the sub differentials of convex functions, and in addition the bibliography has been updated. This popular textbook 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781032946443
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Measure Theory and Fine Properties of Functions
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Measure Theory and Fine Properties of Functions (Textbooks in Mathematics)
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Measure Theory and Fine Properties of Functions, Revised Edition
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Measure Theory and Fine Properties of Functions (Textbooks in Mathematics)
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Hardcover. Condition: Brand New. 2nd revised edition. 344 pages. 9.18x6.12x9.21 inches. In Stock. Seller Inventory # __103294644X
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Measure Theory and Fine Properties of Functions, Revised Edition
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