Opis: Measure Theory and Fine Properties of Functions - Ronald Gariepy, Lawrence Craig Evans

Measure Theory and Fine Properties of Functions, Revised Edition provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. The book emphasizes the roles of Hausdorff measure and capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in n, Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions as well as 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), 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). This revised edition includes countless improvements in notation, format, and clarity of exposition. Also new are several sections describing the pi-lambda theorem, weak compactness criteria in L1, and Young measure methods for weak convergence. In addition, the bibliography has been updated. Topics are carefully selected and the proofs are succinct, but complete. This book provides ideal reading for mathematicians and graduate students in pure and applied mathematics. "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, 2015General 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 Densities 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 Approximation Traces Extensions Sobolev Inequalities Compactness Capacity 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 Traces Extensions 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 (p>n) Convex Functions Second Derivatives a.e. for Convex Functions Whitney's Extension Theorem Approximation by C1 Functions References and Notes Bibliography

Szczegóły: Measure Theory and Fine Properties of Functions - Ronald Gariepy, Lawrence Craig Evans

Tytuł: Measure Theory and Fine Properties of Functions
Autor: Ronald Gariepy, Lawrence Craig Evans
Wydawnictwo: Apple
ISBN: 9781482242386
Rok wydania: 2015
Ilość stron: 313
Oprawa: Twarda
Waga: 0.61 kg

Recenzje: Measure Theory and Fine Properties of Functions - Ronald Gariepy, Lawrence Craig Evans