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Measure and Integration

  • Textbook
  • © 2019

Overview

Authors:
  1. S. Kesavan (emeritus)

    1. Institute of Mathematical Sciences, Chennai, India

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  • Discusses the Riemann integral briefly
  • Drives inspiration from lectures delivered by the author in several leading institutes in India
  • Contains interesting examples and a variety of exercises

Part of the book series: Texts and Readings in Mathematics (TRIM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-viii
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  2. Measure

    • S. Kesavan
    Pages 9-29

  3. The Lebesgue measure

    • S. Kesavan
    Pages 30-53

  4. Measurable functions

    • S. Kesavan
    Pages 54-67

  5. Convergence

    • S. Kesavan
    Pages 68-80

  6. Integration

    • S. Kesavan
    Pages 81-117

  7. Differentiation

    • S. Kesavan
    Pages 118-141

  8. Change of variable

    • S. Kesavan
    Pages 142-155

  9. Product Spaces

    • S. Kesavan
    Pages 156-177

  10. Signed measures

    • S. Kesavan
    Pages 178-195

  11. Lp-spaces

    • S. Kesavan
    Pages 196-234

  12. Back Matter

    Pages 235-240
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Keywords

About this book

This book deals with topics on the theory of measure and integration. It starts with discussion on the Riemann integral and points out certain shortcomings, which motivate the theory of measure and the Lebesgue integral. Most of the material in this book can be covered in a one-semester introductory course. An awareness of basic real analysis and elementary topological notions, with special emphasis on the topology of the n-dimensional Euclidean space, is the pre-requisite for this book. Each chapter is provided with a variety of exercises for the students. The book is targeted to students of graduate- and advanced-graduate-level courses on the theory of measure and integration.

Authors and Affiliations

  • Institute of Mathematical Sciences, Chennai, India

    S. Kesavan (emeritus)

About the author

S. KESAVAN is former professor at the Institute of Mathematical Sciences, Chennai, and adjunct faculty at the Indian Institute of Technology Madras, Chennai, India. He started his career at the Tata Institute of Fundamental Research Centre for Applicable Mathematics (TIFR-CAM), Bangalore, India, in 1973. He has also been associated with the Chennai Mathematical Institute, where he was deputy director during 2007-2010 and he is currently adjunct professor at the Indian Institute of Technology, Madras. He earned his PhD from Université Pierre-et-Marie-Curie, Paris, in 1979. He is a fellow of the National Academy of Sciences, India, at Allahabad and the Indian Academy of Sciences, Bangalore, India. He is a life member of the National Board for Higher Mathematics, since 2000, Indian Mathematical Society, International Society for the Interaction of Mechanics and Mathematics (ISIMM), Indian Society of Industrial and Applicable Mathematics (ISIAM), Ramanujan Mathematical Society, American Mathematical Society and an elected fellow of the Forum d’Analystes, Chennai. He was also the Secretary (Grant Selection) of the Commission for Developing Countries of the International Mathematical Union, during 2011-2014 and 2015-2018. He has published four books and authored over 50 research articles, apart from several contributions to conference proceedings and popular articles. His research interests are in partial differential equations, homogenization, control theory, and isoperimetric inequalities.

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