Fractals and Rectifiability. Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces.

Fractals and Rectifiability. Mathematika, Vol. 42, Issue. 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 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 main theme of this book is the study of geometric properties of general sets and measures in euc lidean space. Series: Cambridge Studies in Advanced Mathematics (Book 44). Paperback: 356 pages. 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 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.

Электронная книга "Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability", Pertti Mattila. Эту книгу можно прочитать в Google Play Книгах на компьютере, а также на устройствах Android и iOS. Выделяйте текст, добавляйте закладки и делайте заметки, скачав книгу "Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability" для чтения в офлайн-режиме.

His book Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability is now .

His book Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability is now a widely cited and a standard textbook in this field. Mattila has been the leading figure on creating the geometric measure theory school in Finland and the Mathematics Genealogy Project cites he has supervised so far 15 PhD students in the field. He obtained his PhD from the University of Helsinki under the supervision of Jussi Väisälä in 1973.

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Intersections of general sets 14. Tangent measures and densities 15. Rectifiable sets and approximate . Rectifiable sets and approximate tangent planes 16. Rectifiability, weak linear approximation and tangent measures 17. Rectifiability and densities 18. Rectifiability and orthogonal projections 19. Rectifiability and othogonal projections 19. Rectifiability and analytic capacity in the complex plane 20. Rectifiability and singular intervals References List of notation Index of terminology.

The focus of this book is geometric properties of general sets and measures in Euclidean . Series: Cambridge Studies in Advanced Mathematics. Categories: Mathematics.

Cambridge Studies in Advanced Mathematics (Paperback). By (author) Pertti Mattila.