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Essentials of Integration Theory for Analysis

  • Daniel W. Stroock

Part of the Graduate Texts in Mathematics book series (GTM, volume 262)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Daniel W. Stroock
    Pages 1-27
  3. Daniel W. Stroock
    Pages 28-61
  4. Daniel W. Stroock
    Pages 62-99
  5. Daniel W. Stroock
    Pages 100-112
  6. Daniel W. Stroock
    Pages 113-145
  7. Daniel W. Stroock
    Pages 146-173
  8. Daniel W. Stroock
    Pages 174-202
  9. Back Matter
    Pages 235-243

About this book

Introduction

Essentials of Integration Theory for Analysis is a substantial revision of the best-selling Birkhäuser title by the same author,  A Concise Introduction to the Theory of Integration. Highlights of this new textbook for the GTM series include revisions to Chapter 1 which add a section about the rate of convergence of Riemann sums and introduces a discussion of the Euler–MacLauren formula.  In Chapter 2, where Lebesque’s theory is introduced, a construction of the countably additive measure is done with sufficient generality to cover both Lebesque and Bernoulli  measures. Chapter 3 includes a proof of Lebesque’s differential theorem for all monotone functions and the concluding chapter has been expanded to include a proof of Carathéory’s  method for constructing measures and his result is applied to the construction of the Hausdorff measures.

This new gem is appropriate as a text for a one-semester graduate course in integration theory and is complimented by the addition of several problems related to the new material.  The text is also highly useful for self-study. A complete solutions manual is available for instructors who adopt the text for their courses.

Additional publications by Daniel W. Stroock:  An Introduction to Markov Processes,  ©2005 Springer (GTM 230), ISBN: 978-3-540-23499-9; A Concise Introduction to the Theory of Integration, © 1998 Birkhäuser Boston, ISBN: 978-0-8176-4073-6;  (with S.R.S. Varadhan) Multidimensional Diffusion Processes, © 1979 Springer (Classics in Mathematics), ISBN: 978-3-540-28998-2.

Keywords

Hausdorff measure Riemann integration Riemann sum integration theory measure and integration

Authors and affiliations

  • Daniel W. Stroock
    • 1
  1. 1., Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1135-2
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1134-5
  • Online ISBN 978-1-4614-1135-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site