Integration and Modern Analysis

1. Auflage. 2009
ISBN: 978-0-8176-4306-5
Verlag: Birkhauser Boston

Buch, Englisch, 575 Seiten, Format (B × H): 164 mm x 242 mm, Gewicht: 1006 g

Reihe: Birkhäuser Advanced Texts Basler Lehrbücher

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Benedetto, John J

Czaja, Wojciech

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis

Inhaltsverzeichnis

Classical Real Variables.- Lebesgue Measure and General Measure Theory.- The Lebesgue Integral.- The Relationship between Differentiation and Integration on.- Spaces of Measures and the Radon#x2013;Nikodym Theorem.- Weak Convergence of Measures.- Riesz Representation Theorem.- Lebesgue Differentiation Theorem on.- Self-Similar Sets and Fractals.- Functional Analysis.- Fourier Analysis.