Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability (Cambridge Studies in Advanced Mathematics, Series Number 44) - Hardcover

Mattila, Pertti

Hardcover

ISBN 10: 0521465761 ISBN 13: 9780521465762

Publisher: Cambridge University Press, 1995

Synopsis

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.

About this title

Review

"Provides a unified theory for the study of the topic and develops the main tools used in its study including theorems, Hausdorff measures, and their relations to Riesz capacities and Fourier transforms." Book News, Inc.

Book Description

Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean space. Examples to which this theory applies include fractal-type objects such as strange attractors for dynamical systems, and those fractals used as models in the sciences.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1995
• ISBN 10: 0521465761
• ISBN 13: 9780521465762
• Binding: Hardcover
• Language: English
• Number of pages: 355