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Essentials of Measure Theory

  • Carlos S. Kubrusly

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introduction to Measures and Integration

    1. Front Matter
      Pages 1-1
    2. Carlos S. Kubrusly
      Pages 3-21
    3. Carlos S. Kubrusly
      Pages 23-39
    4. Carlos S. Kubrusly
      Pages 41-55
    5. Carlos S. Kubrusly
      Pages 57-69
    6. Carlos S. Kubrusly
      Pages 71-87
    7. Carlos S. Kubrusly
      Pages 89-107
    8. Carlos S. Kubrusly
      Pages 109-129
    9. Carlos S. Kubrusly
      Pages 131-157
    10. Carlos S. Kubrusly
      Pages 159-179
  3. Measures on Topological Spaces

    1. Front Matter
      Pages 181-181
    2. Carlos S. Kubrusly
      Pages 183-200
    3. Carlos S. Kubrusly
      Pages 201-222
    4. Carlos S. Kubrusly
      Pages 223-246
    5. Carlos S. Kubrusly
      Pages 247-267
  4. Back Matter
    Pages 269-279

About this book

Introduction

​Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces.

The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. The entire book contains collections of suggested readings at the end of each chapter in order to highlight alternate approaches, proofs, and routes toward additional results.

With modest prerequisites, this text is intended to meet the needs of a contemporary course in measure theory for mathematics students and is also accessible to a wider student audience, namely those in statistics, economics, engineering, and physics. Part I may be also accessible to advanced undergraduates who fulfill the prerequisites which include an introductory course in analysis, linear algebra (Chapter 5 only), and elementary set theory.

Keywords

Borel measure Haar measure Lebesgue measure Lp spaces Riesz representation theorem measurable functions measure and integration measure theory textbook adoption measures on topological spaces monotone convergence theorem real-valued functions sigma-algebra

Authors and affiliations

  • Carlos S. Kubrusly
    • 1
  1. 1.Electrical Engineering DepartmentCatholic University of Rio de JaneiroRio de JaneiroBrazil

Bibliographic information

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