Integration and modern analysis
Author(s)
Bibliographic Information
Integration and modern analysis
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser, c2009
- : hbk
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Description and Table of Contents
Description
This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonne-Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.
Table of Contents
Preface.-Classical real variables.-Lebesgue measure and general measure theory.-The Lebesgue integral.-The relationship between differentiation and integration on R.-Spaces of measures and the Radon-Nikodym theorem.-Weak convergence of measures.-Riesz representation theorem.-Lebesgue differentiation theorem on Rd.-Self-similar sets and fractals.-Appendix I: Functional analysis.-Appendix II: Fourier Analysis.-References.-Index.
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