In this chapter we shall introduce some general measure-theoretic concepts, terminology, and results which will be needed later on.
An edition of Geometry of Sets and Measures in Euclidean Spaces
(1995)
Geometry of sets and measures in Euclidean spaces
fractals and rectifiability
by Pertti Mattila
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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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Previews available in: English
| Edition | Availability |
|---|---|
1
Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
2012, Cambridge University Press
in English
051162381X 9780511623813
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2
Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
April 1999, Cambridge University Press
Paperback
in English
- New Ed edition
0521655951 9780521655958
|
zzzz
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3
Geometry of sets and measures in Euclidean spaces: fractals and rectifiability
1995, Cambridge University Press
in English
0521465761 9780521465762
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Includes bibliographical references (p. 305-333) and indexes.
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