Publisher description for The geometry of fractal sets / K.J. Falconer.
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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. 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 history is applicable and contains discussions of curves of fractional dimension, self-similar sets, strange attractors, and examples from number theory, and convexity.
Library of Congress subject headings for this publication: Fractals, Geometric measure theory