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

The focus of this book is 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 for the subject and develops all the main tools used in its study, 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 Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of Euclidean space possessing many of the properties of smooth surfaces.

About this title

Book Description

The main theme of this book is the study of geometric properties of general sets and measures in euc lidean 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.The author provides a firm and unified foundation for the subject and develops all the main tools used in its study, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. Thus the book is essentially self-contained for graduate students in mathematics; it is primarily targetted at them and researchers.The last third of the book is devoted to the Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space possessing many of the properties of smooth surfaces. These sets have wide application; for example they are central in the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied.

About the Author

Pertti Mattila is Professor of Mathematics at the University of Helsinki and an expert in geometric measure theory. He has authored the book Geometry of Sets and Measures in Euclidean Spaces as well as more than 80 other scientific publications.

Edition details

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