# Essentials of Integration Theory for Analysis

Part of the Graduate Texts in Mathematics book series (GTM, volume 262)

Part of the Graduate Texts in Mathematics book series (GTM, volume 262)

*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.* *

Hausdorff measure Riemann integration Riemann sum integration theory measure and integration

- DOI https://doi.org/10.1007/978-1-4614-1135-2
- Copyright Information Springer Science+Business Media, LLC 2011
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4614-1134-5
- Online ISBN 978-1-4614-1135-2
- Series Print ISSN 0072-5285
- About this book