Integration and Modern Analysis

• Main Authors: Benedetto, John J. (Author), Czaja, Wojciech (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2009.
• Series: Birkhäuser Advanced Texts / Basler Lehrbücher
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Analysis.

A paean to twentieth century analysis, this modern text has several important themes and key features which set it apart from others on the subject. A major thread throughout is the unifying influence of the concept of absolute continuity on differentiation and integration. This leads to fundamental...

Table of Contents:

• 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.