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Synopsis
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 Description
A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
Review
"...by far the most accessible mathematical account available and therefore is an invaluable addition to the literature." Science
"...a lovely introduction to the mathematics of fractal sets for the pure mathematician." American Mathematical Monthly
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The Geometry of Fractal Sets (Cambridge Tracts in Mathematics)
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The Geometry of Fractal Sets (Cambridge Tracts in Mathematics, Series Number 85)
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The Geometry of Fractal Sets (Cambridge Tracts in Mathematics, Series Number 85)
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The Geometry of Fractal Sets (Cambridge Tracts in Mathematics)
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The Geometry of Fractal Sets
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The Geometry of Fractal Sets [Cambridge Tracts in Mathematics 85]
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