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The Geometry of Fractal Sets : Cambridge Tracts in Mathematics (Paperback) - Kenneth J. Falconer

The Geometry of Fractal Sets

Cambridge Tracts in Mathematics (Paperback)

By: Kenneth J. Falconer, B. Bollobas (Editor), W. Fulton (Editor), A. Katok (Editor), F. Kirwan (Editor)

Paperback Published: 22nd September 1986
ISBN: 9780521337052
Number Of Pages: 180

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This book contains a rigorous mathematical treatment of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Questions of local density and the existence of tangents of such sets are studied, as well as the dimensional properties of their projections in various directions. In the case of sets of integral dimension the dramatic differences between regular 'curve-like' sets and irregular 'dust like' sets are exhibited. The theory is related by duality to Kayeka sets (sets of zero area containing lines in every direction). The final chapter includes diverse examples of sets to which the general theory is applicable: discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, convexity and so on. There is an emphasis on the basic tools of the subject such as the Vitali covering lemma, net measures and Fourier transform methods.

'This book is filled with the geometric jewels of fractional and integral Hausdorff dimension. It contains a much-needed unified notation and includes many recent results with simplified proofs. The theory is classically and rigorously presented with applications only alluded to in the introduction. Each chapter contains a short and important problem set. This is a lovely introduction to the mathematics of fractal sets for the pure mathematician.' American Mathematical Monthly

Measure and dimension
Basic density properties
Structure of sets of integral dimension
Structure of sets of non-integral dimension
Comparable net measures
Projection properties
Besicovitch and Kakeya sets
Miscellaneous examples of fractal sets
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521337052
ISBN-10: 0521337054
Series: Cambridge Tracts in Mathematics (Paperback)
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 180
Published: 22nd September 1986
Country of Publication: GB
Dimensions (cm): 22.81 x 15.44  x 1.14
Weight (kg): 0.28