Essentials of Integration Theory for Analysis
Authors: Stroock, Daniel W.
 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
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 About this Textbook

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. 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 onesemester 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 selfstudy. 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: 9783540234999; A Concise Introduction to the Theory of Integration, © 1998 Birkhäuser Boston, ISBN: 9780817640736; (with S.R.S. Varadhan) Multidimensional Diffusion Processes, © 1979 Springer (Classics in Mathematics), ISBN: 9783540289982.
 About the authors

Daniel W. Stroock is now Emeritus professor of the mathematics department at MIT. He is a renowned mathematician in the areas of analysis and probability theory and stochastic processes.
Prof. Stroock has had an active career in both the research and administrative levels of academia. From 20022006, he was selected the first holder of the second Simons Professorship of Mathematics. He has served as Chair of the Pure Math Committee from 19951997; a board member of the National Research Council. He has also chaired various committees of the AMS and was a nominee for AMS President in 1999. In 1996, the AMS awarded Dan Stroock (jointly with S. Varadhan), the Leroy P. Steele Prtize for his seminal contributions to research in stochastic equations. Prof. Stroock is a member of both the American Academy of Arts and Sciences and the National Academy of Sciences.
 Reviews

From the reviews:
“This volume is an appropriate text for a onesemester graduate course in integration theory and is complemented by the addition of several problems related to the new material. … This volume should become a new relevant reference for integration theory. It will help the reader to sharpen his/her sensitivity to issues of measure theory, and to renew his/hers expertise in integration theory. … warmly recommends the book with confidence to anyone who is interested in understanding modern integration theory.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1228, 2012)
“This is a book in measure theory at the graduate level. … The presentation is clear and concise, and detailed proofs are given. … Each section also contains a long and useful list of exercises. … The book is certainly well suited to the serious student or researcher in another field who wants to learn the topic. … the book could be used by lecturers who want to illustrate a standard graduate course in measure theory by interesting examples from other areas of analysis.” (Lars Olsen, Mathematical Reviews, Issue 2012 h)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Essentials of Integration Theory for Analysis
 Authors

 Daniel W. Stroock
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 262
 Copyright
 2011
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media, LLC
 eBook ISBN
 9781461411352
 DOI
 10.1007/9781461411352
 Hardcover ISBN
 9781461411345
 Softcover ISBN
 9781461429883
 Series ISSN
 00725285
 Edition Number
 1
 Number of Pages
 XII, 244
 Topics