Essentials of integration theory for analysis
 Author/Creator
 Stroock, Daniel W.
 Language
 English.
 Imprint
 New York : Springer, c2011.
 Physical description
 xi, 243 p. ; 24 cm.
 Series
 Graduate texts in mathematics ; 262.
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Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 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 RadonNikodym Theorem, Daniell Integration, and Caratheodory's Extension Theorem.Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 'A Concise Introduction to the Theory of Integration' was once a bestselling Birkhauser 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 EulerMacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include a proof of Caratheory'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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Responsibility
 Daniel W. Stroock.
 Series
 Graduate texts in mathematics ; 262
 ISBN
 9781461411345
 1461411343