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Integration and Modern Analysis

Integration and Modern Analysis

Hardcover

Series: Birkhäuser Advanced Texts Basler Lehrbücher

General Mathematics

ISBN10: 0817643060
ISBN13: 9780817643065
Publisher: Springer Nature
Published: Oct 16 2009
Pages: 575
Weight: 2.25
Height: 1.50 Width: 6.50 Depth: 9.30
Language: English

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 Dieudonné-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.

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General Mathematics