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Essentials of Integration Theory for Analysis

By Daniel W. Stroock

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Essentials of Integration Theory for Analysis is a substantial revision of the bestselling Birkhäuser title by the same author,  A Concise Introduction to the Theory of Integration. 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.

Full Description

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  • ISBN13: 978-1-4614-1134-5
  • 254 Pages
  • Publication Date: August 2, 2011
  • Available eBook Formats: PDF

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Full Description
‘A Concise Introduction to the Theory of Integration’ was once a best-selling Birkhäuser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. This is a beautiful topic which is not often covered. The treatment of surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include a proof of Carathéory's method for constructing measures; his result is applied to the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material.
Table of Contents

Table of Contents

  1. Preface.
  2. 1. The Classical Theory.
  3. 2. Measures.
  4. 3. Lebesgue Integration.
  5. 4. Products of Measures.
  6. 5. Changes of Variable.
  7. 6. Basic Inequalities and Lebesgue Spaces.
  8. 7. Hilbert Space and Elements of Fourier Analysis.
  9. 8. The Radon
  10. Nikodym Theorem, Daniell Integration, and Carathéodory's Extension Theorem.
  11. Index.
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