The Geometry of Fractal Sets ( Cambridge Tracts in Mathematics 85 )

Cambridge University Press, Cambridge, Great Britain, 1990. reprint. Softcover. Very Good Condition. 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. The author has brought together much of this area of geometric measure theory, which has been previously only available in tactical papers. Some of the proofs have been simplified, new material is included and further developments are surveyed. – Rear panel blurb Size: 8vo - over 7¾" - 9¾" tall. 180 pages. Please refer to accompanying picture (s). Quantity Available: 1. Shipped Weight: Under 500 grams. Category: mathematics; ISBN: 0521337054. ISBN/EAN: 9780521337052. Inventory No: 0258356. . 9780521337052