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Mathematics - Analysis | Essentials of Integration Theory for Analysis

Essentials of Integration Theory for Analysis

Series: Graduate Texts in Mathematics, Vol. 262

Stroock, Daniel W.

2011, XII, 244 p.

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  • 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

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.

Content Level » Graduate

Keywords » Hausdorff measure - Riemann integration - Riemann sum - integration theory - measure and integration

Related subjects » Analysis

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