Essentials of Integration Theory for Analysis

丛 书 名：Graduate Texts in Mathematics

版本说明：1

作     者：Stroock, Daniel W. 

I S B N：(纸本) 9781461411345 

出 版 社：springer 

出 版 年：2011年

馆 藏 号：201993371...

摘      要：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 textbookNew material is complemented by the addition of several new problemsEssentials 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 *** 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.