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 . 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 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.

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 Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

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Daniel W. Stroock is Emeritus professor of mathematics at MIT. He is a respected mathematician in the areas of analysis, probability theory and stochastic processes. Prof. Stroock has had an active career in both the research and education. From 2002 until 2006, he was the first holder of the second Simons Professorship of Mathematics. In addition, he has held several administrative posts, some within the university and others outside. In 1996, the AMS awarded him together with his former colleague jointly S.R.S. Varadhan the Leroy P. Steele Prize for seminal contributions to research in stochastic processes. Finally, he is a member of both the American Academy of Arts and Sciences, the National Academy of Sciences and a foreign member of the Polish Academy of Arts and Sciences.

Inhalt
-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.