
Measure Theory & Fine Properties of Functions
CRC Press
1st Edition
Published on 18. December 1991
Book
Hardback
290 pages
978-0-8493-7157-8 (ISBN)
Description
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation.
The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions).
Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions).
Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
More details
Language
English
Place of publication
Bosa Roca
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional and scholarly
Professional
Dimensions
Height: 234 mm
Width: 156 mm
Weight
552 gr
ISBN-13
978-0-8493-7157-8 (9780849371578)
Schweitzer Classification
Persons
LawrenceCraig Evans
Content
Preface, 1: General Measure Theory, 2: Hausdorff Measure, 3: Area and Coarea Formulas, 4: Sobolev Functions, 5: BV Functions and Sets of Finite Perimeter, 6: Differentiability and Approximation by C1 Functions, Bibliography, Notation, Index