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Measure theory and fine properties of functions / Lawrence C. Evans and Ronald F. Gariepy.

By: Contributor(s): Material type: TextTextSeries: Textbooks in mathematicsPublication details: Boca Raton : CRC Press, ©2015.Edition: Revised editionDescription: xiv, 299 p. : illustrations ; 24 cmISBN:
  • 9781482242386 (hardback : acidfree paper)
Subject(s): DDC classification:
  • 515.42 23 Ev92
Contents:
1. General Measure Theory -- 2. Hausdorff Measures -- 3. Area and Coarea Formulas -- 4. Sobolev Functions -- 5. Functions of Bounded Variation, Sets of Finite Perimeter -- 6. Differentiability, Approximation by C1 Functions.
Summary: 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.
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Includes bibliographical references and index.

1. General Measure Theory --
2. Hausdorff Measures --
3. Area and Coarea Formulas --
4. Sobolev Functions --
5. Functions of Bounded Variation, Sets of Finite Perimeter --
6. Differentiability, Approximation by C1 Functions.

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.

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