Advertisement

Integration and Modern Analysis

  • John J. Benedetto
  • Wojciech Czaja

Part of the Birkhäuser Advanced Texts / Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xix
  2. John J. Benedetto, Wojciech Czaja
    Pages 1-35
  3. John J. Benedetto, Wojciech Czaja
    Pages 37-94
  4. John J. Benedetto, Wojciech Czaja
    Pages 95-164
  5. John J. Benedetto, Wojciech Czaja
    Pages 165-218
  6. John J. Benedetto, Wojciech Czaja
    Pages 219-276
  7. John J. Benedetto, Wojciech Czaja
    Pages 277-320
  8. John J. Benedetto, Wojciech Czaja
    Pages 321-357
  9. John J. Benedetto, Wojciech Czaja
    Pages 359-406
  10. John J. Benedetto, Wojciech Czaja
    Pages 407-439
  11. John J. Benedetto, Wojciech Czaja
    Pages 441-485
  12. John J. Benedetto, Wojciech Czaja
    Pages 487-528
  13. Back Matter
    Pages 529-575

About this book

Introduction

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 results such as the Dieudonné–Grothendieck theorem and other intricate developments dealing with weak convergence of measures.

Key Features:

* Fascinating historical commentary interwoven into the exposition;

* Hundreds of problems from routine to challenging;

* Broad mathematical perspectives and material, e.g., in harmonic analysis and probability theory, for independent study projects;

* Two significant appendices on functional analysis and Fourier analysis.

Key Topics:

* In-depth development of measure theory and Lebesgue integration;

* Comprehensive treatment of connection between differentiation and integration, as well as complete proofs of state-of-the-art results;

* Classical real variables and introduction to the role of Cantor sets, later placed in the modern setting of self-similarity and fractals;

* Evolution of the Riesz representation theorem to Radon measures and distribution theory;

* Deep results in modern differentiation theory;

* Systematic development of weak sequential convergence inspired by theorems of Vitali, Nikodym, and Hahn–Saks;

* Thorough treatment of rearrangements and maximal functions;

* The relation between surface measure and Hausforff measure;

* Complete presentation of Besicovich coverings and differentiation of measures.

Integration and Modern Analysis will serve advanced undergraduates and graduate students, as well as professional mathematicians. It may be used in the classroom or self-study.

Keywords

Complex variables Distribution Lebesgue differentiation theorem Maximum Measure theory Real analysis Riesz representation theorem calculus differential equation functional analysis measure

Authors and affiliations

  • John J. Benedetto
    • 1
  • Wojciech Czaja
    • 2
  1. 1.Dept. MathematicsUniversity of MarylandCollege ParkU.S.A.
  2. 2.Dept. MathematicsUniversity of MarylandCollege ParkU.S.A.

Bibliographic information