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A Concise Introduction to the Theory of Integration

  • Textbook
  • © 1994

Overview

Authors:
  1. Daniel W. Stroock

    1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
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  2. The Classical Theory

    • Daniel W. Stroock
    Pages 1-18

  3. Lebesgue’s Measure

    • Daniel W. Stroock
    Pages 19-33

  4. Lebesgue Integration

    • Daniel W. Stroock
    Pages 34-67

  5. Products of Measures

    • Daniel W. Stroock
    Pages 68-79

  6. Changes of Variable

    • Daniel W. Stroock
    Pages 80-113

  7. Some Basic Inequalities

    • Daniel W. Stroock
    Pages 114-138

  8. A Little Abstract Theory

    • Daniel W. Stroock
    Pages 139-158

  9. Back Matter

    Pages 159-184
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Keywords

About this book

This little book is the outgrowth of a one semester course which I have taught for each of the past four years at M. 1. T. Although this class used to be one of the standard courses taken by essentially every first year gradu­ ate student of mathematics, in recent years (at least in those when I was the instructor), the clientele has shifted from first year graduate students of mathematics to more advanced graduate students in other disciplines. In fact, the majority of my students have been from departments of engi­ neering (especially electrical engineering) and most of the rest have been economists. Whether this state of affairs is a reflection on my teaching, the increased importance of mathematical analysis in other disciplines, the superior undergraduate preparation of students coming to M. 1. T in mathematics, or simply the lack of enthusiasm that these students have for analysis, I have preferred not to examine too closely. On the other hand, the situation did force me to do a certain amount of thinking about what constitutes an appropriate course for a group of non-mathematicians who are courageous (foolish?) enough to sign up for an introduction to in­ tegration theory offered by the department of mathematics. In particular, I had to figure out what to do about that vast body of material which, in standard mathematics offerings, is "assumed to have been covered in your advanced calculus course".

Reviews

"This is a very attractive textbook… Unusual in many respects, [it] fully achieves its goal, a one-semester, concise but logically complete treatment of abstract integration. It is remarkable that [the author] has accomplished so much in so short a compass."

- Mathematical Reviews (review of the first edition)

"A number of valuable applications and a good collection of problems... A very interesting, well-informed book which draws on recent approaches not found in several commonly used texts."

- Zentralblatt Math (review of the second edition)

"The author succeeded in choosing the right level of generality and showed how a good combination of a measure and integration course and advanced calculus can be done. Strongly recommended to students as well as to teachers."

- EMS Newsletter (review of the second edition)

"...the author is a distinguished probabilist/analyst who has made seminal contributions to the interface of probability theory with PDEs/harmonic analysis/functional analysis; the flavor of all these subjects is brought out in the book, especially in chapters V-VII...[the] book can be highly rewarding, serving as a launching pad for an intensive study of any branch of analysis including probability theory."

--Current Science (review of the third edition)

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

    Daniel W. Stroock

Bibliographic Information

  • Book Title: A Concise Introduction to the Theory of Integration

  • Authors: Daniel W. Stroock

  • DOI: https://doi.org/10.1007/978-1-4757-2300-7

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Daniel W. Stroock 1994

  • eBook ISBN: 978-1-4757-2300-7Published: 14 March 2013

  • Edition Number: 2

  • Number of Pages: VIII, 184

  • Topics: Analysis

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