Measure Theory and Fine Properties of Functions

Evans, Lawrence Craig

ISBN 10: 103294644X / ISBN 13: 9781032946443

Editore: Chapman and Hall/CRC, 2025

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Titolo: Measure Theory and Fine Properties of ...

Casa editrice: Chapman and Hall/CRC

Data di pubblicazione: 2025

Legatura: Rilegato

Condizione: As New

Edizione: seconda edizione

Descrizione articolo

Riassunto:

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.

Informazioni sull?autore:

Lawrence C. Evans, University of California, Berkeley, USA

Ronald F. Gariepy, University of Kentucky, Lexington, USA