Measure Theory and Fine Properties of Functions

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

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English

Chapman & Hall/CRC
04 March 2025

Calculus & mathematical analysis; Applied mathematics

Series: Textbooks in Mathematics

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.

By: Lawrence C. Evans (University of California Berkeley USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 790g
ISBN: 9781032946443
ISBN 10: 103294644X
Series: Textbooks in Mathematics
Pages: 327
Publication Date: 04 March 2025
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

1 Measure Theory 2 Hausdorff Measures 3 Area and Coarea Formulas 4 Sobolev Functions 5 Functions of Bounded Variation, Sets of Finite Perimeter 6 Differentiability, Approximation by C1 Functions

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