Essentials of Integration Theory for Analysis [electronic resource] / by Daniel W. Stroock.

Essentials of Integration Theory for Analysis is a substantial revision of the best-selling Birkhuser 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 EulerMacLauren formula. In Chapter 2, where Lebesques 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 Lebesques differential theorem for all monotone functions and the concluding chapter has been expanded to include a proof of CarathȨorys 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, è2005 Springer (GTM 230), ISBN: 978-3-540-23499-9; A Concise Introduction to the Theory of Integration, è 1998 Birkhuser Boston, ISBN: 978-0-8176-4073-6; (with S.R.S. Varadhan) Multidimensional Diffusion Processes, è 1979 Springer (Classics in Mathematics), ISBN: 978-3-540-28998-2.

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