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Geometry of Sets and Measures in Euclidean Spaces

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by Pertti Mattila
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Geometry of Sets and Measures in Euclidean Spaces by Pertti Mattila

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.

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Ebook Details
Pages: 355
Size: 15.9 MB
Publisher: Cambridge University Press
Date published:   1995
ISBN: 9781316043929 (DRM-PDF)

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Nonfiction > Mathematics > Algebra > Abstract

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Nonfiction > Mathematics > Mathematical Analysis
Nonfiction > Mathematics > Algebra > Abstract

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