Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability
Pertti Mattila
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.
Κατηγορίες:
Έτος:
1995
Εκδότης:
Cambridge University Press
Γλώσσα:
english
Σελίδες:
356
ISBN 10:
0521465761
ISBN 13:
9780521655958
Σειρές:
Cambridge Studies in Advanced Mathematics 44
Αρχείο:
DJVU, 13.02 MB
IPFS:
,
english, 1995