Measure Theory and Fine Properties of Functions

Measure Theory and Fine Properties of Functions

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.


Author
Publisher CRC Press
Release Date
ISBN 9780849371578
Pages 286 pages
Rating 4/5 (70 users)

More Books:

Measure Theory and Fine Properties of Functions
Language: en
Pages: 286
Authors: Lawrence Craig Evans
Categories: Science
Type: BOOK - Published: 1991-12-18 - Publisher: CRC Press

This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff mea
Measure Theory and Fine Properties of Functions, Revised Edition
Language: en
Pages:
Authors: LAWRENCE CRAIG. GARIEPY EVANS (RONALD F.)
Categories:
Type: BOOK - Published: 2023 - Publisher:

Measure Theory and Fine Properties of Functions
Language: en
Pages: 288
Authors: LawrenceCraig Evans
Categories: Mathematics
Type: BOOK - Published: 2018-04-27 - Publisher: Routledge

This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff mea
Measure Theory and Fine Properties of Functions, Revised Edition
Language: en
Pages: 313
Authors: Lawrence Craig Evans
Categories: Mathematics
Type: BOOK - Published: 2015-04-17 - Publisher: CRC Press

Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Eu
Notes on Real Analysis and Measure Theory
Language: en
Pages: 256
Authors: Alexander Kharazishvili
Categories: Mathematics
Type: BOOK - Published: 2022-09-23 - Publisher: Springer Nature

This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion
Function Spaces and Potential Theory
Language: en
Pages: 368
Authors: David R. Adams
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I sha
Real Analysis and Foundations, Second Edition
Language: en
Pages: 474
Authors: Steven G. Krantz
Categories: Mathematics
Type: BOOK - Published: 2004-11-15 - Publisher: CRC Press

Students preparing for courses in real analysis often encounter either very exacting theoretical treatments or books without enough rigor to stimulate an in-dep
Notes on Real Analysis and Measure Theory
Language: en
Pages: 0
Authors: Aleksandr Bežanovič Charazišvili
Categories: Mathematics
Type: BOOK - Published: 2022 - Publisher:

This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion
Measure Theory
Language: en
Pages: 1075
Authors: Vladimir I. Bogachev
Categories: Mathematics
Type: BOOK - Published: 2007-01-15 - Publisher: Springer Science & Business Media

This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanc
Measures, Integrals and Martingales
Language: en
Pages: 404
Authors: René L. Schilling
Categories: Mathematics
Type: BOOK - Published: 2005-11-10 - Publisher: Cambridge University Press

This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.