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Book 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 Besicovitchâs covering theorem, Rademacherâs 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 Aleksandrovâs 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 gradua

Measure Theory and Fine Properties of Functions

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    A Hardback by Lawrence C. Evans

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      Book details

      Publisher CRC Press
      Published 3 April 2025
      ISBN-13 9781032946443
      978-1032946443
      ISBN-10 103294644X
      Also in:
      Mathematics Applied mathematics

      Description

      Book 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 Besicovitchâs covering theorem, Rademacherâs 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 Aleksandrovâs 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 gradua

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