Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
(Book #44 in the Cambridge Studies in Advanced Mathematics Series)
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Book Overview
Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.
Format:Paperback
Language:English
ISBN:0521655951
ISBN13:9780521655958
Release Date:March 1999
Publisher:Cambridge University Press
Length:356 Pages
Weight:1.20 lbs.
Dimensions:0.9" x 6.0" x 8.9"
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