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Measure Theory and Fine Properties of Functions, Revised Edition


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Table of Contents

General Measure Theory
Measures and Measurable Functions
Lusin's and Egoroff's Theorems
Integrals and Limit Theorems
Product Measures, Fubini's Theorem, Lebesgue Measure
Covering Theorems
Differentiation of Radon Measures
Lebesgue Points, Approximate Continuity
Riesz Representation Theorem
Weak Convergence
References and Notes

Hausdorff Measures
Definitions and Elementary Properties
Isodiametric Inequality, Hn=Ln
Functions and Hausdorff Measure
References and Notes

Area and Coarea Formulas
Lipschitz Functions, Rademacher's Theorem
Linear Maps and Jacobians
The Area Formula
The Coarea Formula
References and Notes

Sobolev Functions
Definitions and Elementary Properties
Sobolev Inequalities
Quasicontinuity; Precise Representatives of Sobolev Functions
Differentiability on Lines
References and Notes

Functions of Bounded Variation, Sets of Finite Perimeter
Definitions, Structure Theorem
Approximation and Compactness
Coarea Formula for BV Functions
Isoperimetric Inequalities
The Reduced Boundary
Gauss-Green Theorem
Pointwise Properties of BV Functions
Essential Variation on Lines
A Criterion for Finite Perimeter
References and Notes

Differentiability, Approximation by C1 Functions
Lp Differentiability; Approximate Differentiability
Differentiability a.e. for W1,p
Convex Functions
Second Derivatives a.e. for Convex Functions
Whitney's Extension Theorem
Approximation by C1
References and Notes


About the Author

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


"This is a new revised edition of a very successful book dealing with measure theory in Rn and some special properties of functions, usually omitted from books dealing with abstract measure theory, but which a working mathematician analyst must know. ... The book is clearly written with complete proofs, including all technicalities. ... The new edition benefits from LaTeX retyping, yielding better cross-references, as well as numerous improvements in notation, format, and clarity of exposition. The bibliography has been updated and several new sections were added ... this welcome, updated, and revised edition of a very popular book will continue to be of great interest for the community of mathematicians interested in mathematical analysis in Rn."
-Studia Universitatis Babes-Bolyai Mathematica, 60, 2015

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