Advertisement

Measure, Topology, and Fractal Geometry

  • Gerald Edgar

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Gerald Edgar
    Pages 1-40
  3. Gerald Edgar
    Pages 41-84
  4. Gerald Edgar
    Pages 85-116
  5. Gerald Edgar
    Pages 117-136
  6. Gerald Edgar
    Pages 137-164
  7. Gerald Edgar
    Pages 165-224
  8. Gerald Edgar
    Pages 225-250
  9. Back Matter
    Pages 251-278

About this book

Introduction

For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so that now it is often treated on a par with the Hausdorff measure. The topological dimensions were rearranged for Chapter 3, so that the covering dimension is the major one, and the inductive dimensions are the variants. A "reduced cover class" notion was introduced to help in proofs for Method I or Method II measures. Research results since 1990 that affect these elementary topics have been taken into account. Some examples have been added, including Barnsley leaf and Julia set, and most of the figures have been re-drawn.

 

From reviews of the First Edition:

 "...there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high-school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology...the book also contains many good illustrations of fractals..."

 - Mathematics Teaching

 "The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples."

 - Christoph Bandt, Mathematical Reviews

 "...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. [For such students] the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out."

 - H.Haase, Zentralblatt

Keywords

Fractal Self-similarity fractal dimension measure theory similarity

Editors and affiliations

  • Gerald Edgar
    • 1
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-74749-1
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-74748-4
  • Online ISBN 978-0-387-74749-1
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site