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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.

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Book Details

ISBN: 9780521337052
ISBN-10: 0521337054
Format: Paperback
(228mm x 152mm x 11mm)
Pages: 180
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 24-Jul-1986
Country of Publication: United Kingdom

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