Essentials of Integration Theory for Analysis

Essentials of Integration Theory for Analysis

by Daniel W. Stroock


View All Available Formats & Editions
Choose Expedited Shipping at checkout for guaranteed delivery by Monday, February 24
6 New & Used Starting at $60.90


‘A Concise Introduction to the Theory of Integration’ was once a best-selling Birkhäuser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. This is a beautiful topic which is not often covered. The treatment of surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include a proof of Carathéory's method for constructing measures; his result is applied to the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material.

Product Details

ISBN-13: 9781461429883
Publisher: Springer New York
Publication date: 10/24/2013
Series: Graduate Texts in Mathematics , #262
Edition description: 2011
Pages: 244
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

About the Author

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 careerin both the research and administrative levels of academia. From 2002-2006, he was selected the first holder of the second Simons Professorship of Mathematics. He has served as Chair of the Pure Math Committee from 1995-1997; 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.

Table of Contents

-Preface.-1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. The Radon-Nikodym Theorem, Daniell Integration, and Carathéodory's Extension Theorem.-Index.

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews