Integration and Modern Analysis

• Main Authors: Benedetto, John J. (Author), Czaja, Wojciech. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2009.
• Series: Birkhũser Advanced Texts / Basler Lehrb<U+00fc>cher
• Subjects: Mathematics.; Global analysis (Mathematics).; Functions of complex variables.; Analysis.; Functions of a Complex Variable.; Measure and Integration.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4656-1

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:

• 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<U+0013>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.