Measure, Topology, and Fractal Geometry

Hardcover | November 26, 2007

byGerald Edgar

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Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

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From the Publisher

Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such top...

From the Jacket

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 ...

Format:HardcoverDimensions:288 pages, 9.25 × 6.1 × 0.04 inPublished:November 26, 2007Publisher:SpringerLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387747486

ISBN - 13:9780387747484

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Table of Contents

Preface.- Fractal Examples.- Metric Topology.- Topological Dimension.- Self-similarity.- Measure Theory.- Fractal Dimension.- Additional Topics.- Appendix.- Index.

Editorial Reviews

From the reviews of the second edition:"As a non-specialist, I found this book very helpful. It gave me a better understanding of the nature of fractals, and of the technical issues involved in the theory. I think it will be valuable as a textbook for undergraduate students in mathematics, and also for researchers wanting to learn fractal geometry from scratch. The material is well-organized and the proofs are clear; the abundance of examples is an asset for a book on measure theory and topology." (Fabio Mainardi, MathDL, February, 2008)"This is the second edition of a well-known textbook in the field . . The book may serve as a textbook for a one-semester (advanced) undergraduate course in mathematics. . the book is also suitable for readers interested in theoretical fractal geometry coming from other disciplines (e.g. physics, computer sciences) with a basic knowledge of mathematics. The presentation of the material is appealing . and the style is clear and motivating. . the book will remain as a standard reference in the field." (José-Manuel Rey, Zentralblatt MATH, Vol. 1152, 2009)