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 ...
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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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Good. Size: 19 to 25 cm tall, Octavo, (8vo); Posted within 1 working day. 1st class tracked post to the UK, Airmail tracked worldwide. Robust recyclable packaging.
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Very Good in No d/j as Published jacket. Size: 8vo-over 7¾"-9¾" tall; Type: Book N.B. Small plain label to inside front cover. Crease to top right corner of front cover.
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Fair. AGe wear. Foxing. TAnned pages. Cover is worn and torn. Open Books is a nonprofit social venture that provides literacy experiences for thousands of readers each year through inspiring programs and creative capitalization of books.
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