Geometric measure theory

Geometric measure theory: a beginner's guide

by Morgan, Frank, (Professor of Mathematics, Williams College)

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Title Statements

  • Full title :Geometric measure theory : a beginner's guide / Frank Morgan ; illustrated by James F. Bredt.

Edition Statements

  • Publication Date:2016.
  • Edition:5th edition

Publication Statements

  • Publisher(s):Elsevier Ltd
  • Place of Publication:Amsterdam
  • Language:eng
  • Publication Date:2016.

The Physical Object

  • Description:1 online resource

Edition Identifiers

  • ISBN:9780128045275, 0128045272
  • oclc:ocn948810773
  • LC Classification:QA312
  • Dewey Decimal:515/.42

Table of Contents

Front Cover ; Dedication ; Geometric Measure Theory: A Beginner's Guide ; Copyright ; Contents; Preface; Part I: Basic Theory; Chapter 1: Geometric Measure Theory ; 1.1 Archetypical Problem; 1.2 Surfaces as Mappings; 1.3 The Direct Method; 1.4 Rectifiable Currents; 1.5 The Compactness Theorem; 1.6 Advantages of Rectifiable Currents; 1.7 The Regularity of Area-Minimizing Rectifiable Currents ; 1.8 More General Ambient Spaces; Chapter 2: Measures ; 2.1 Definitions; 2.2 Lebesgue Measure; 2.3 Hausdorff Measure ; 2.4 Integral-Geometric Measure; 2.5 Densities ; 2.6 Approximate Limits.

2.7 Besicovitch Covering Theorem 2.8 Corollary; 2.9 Corollary; 2.10 Corollary; Exercises; Chapter 3: Lipschitz Functions and Rectifiable Sets ; 3.1 Lipschitz Functions; 3.2 Rademacher's Theorem ; 3.3 Approximation of a Lipschitz Function by a C1 Funcation ; 3.4 Lemma (Whitney's Extension Theorem) ; 3.5 Proposition ; 3.6 Jacobians; 3.7 The Area Formula ; 3.8 The Coarea Formula ; 3.9 Tangent Cones; 3.10 Rectifiable Sets ; 3.11 Proposition ; 3.12 Proposition ; 3.13 General Area-Coarea Formula ; 3.14 Product of Measures ; 3.15 Orientation; 3.16 Crofton's Formula ; 3.17 Structure Theorem.

ExercisesChapter 4: …

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Subjects

Geometric measure theory MATHEMATICS -- Calculus Mathematics -- Mathematical Analysis Théorie de la mesure géométrique

Writers

Morgan, Frank, (Professor of Mathematic… Bredt, James F.

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