The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. 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;

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

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.

Refocus and substantial revision of previous successful publication "A Concise Introduction to the Theory of Integration" by D.W. Stroock (Birkhauser) Separate solutions manual available to those who adopt the textbook New material is complemented by the addition of several new problems Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

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