Includes bibliographical references (pages 289-291).
CONTENTS NOTE
Text of Note
General Measure Theory -- Hausdorff Measures -- Area and Coarea Formulas -- Sobolev Functions -- Functions of Bounded Variation, Sets of Finite Perimeter -- Differentiability, Approximation by C1 Functions.
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SUMMARY OR ABSTRACT
Text of Note
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 ℝn, 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 complet.