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

Mattila, Pertti

ISBN 10: 0521655951 / ISBN 13: 9780521655958

Editore: Cambridge University Press, 1999

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Dati bibliografici

Titolo: Geometry of Sets and Measures in Euclidean ...

Casa editrice: Cambridge University Press

Data di pubblicazione: 1999

Legatura: Brossura

Condizione: Good

Descrizione articolo

Riassunto:

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.

Recensione:

"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.