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Measure Theory and Fine Properties of Functions

Measure Theory and Fine Properties of Functions

Hardcover

Series: Textbooks in Mathematics

CalculusGeneral Mathematics

ISBN10: 103294644X
ISBN13: 9781032946443
Publisher: CRC Press
Published: Mar 4 2025
Pages: 327
Weight: 1.44
Height: 0.81 Width: 6.14 Depth: 9.21
Language: English

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).

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General Mathematics