Geometry of sets and measures in euclidean spaces

By:

Mattila, Pertti

Material type: Book

BookSeries: Cambridge studies in advanced mathematics ; 44Publication details: Cambridge: Cambridge University Press, 1999.Description: xii, 343 p. : ill. ; pb, 24 cmISBN:

9780521655958

Subject(s):

DDC classification:

515.42 MAT

Summary: 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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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515.42 MAT (Browse shelf(Opens below))	1	Available		030105

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Previous	515.42 DAJ Ergodic theory of numbers	515.42 HAL Measure theory	515.42 KES Measure and integration	515.42 MAT Geometry of sets and measures in euclidean spaces	515.43 BLE Asymptotic expansions of integrals	515.43 ROS Varieties of integration	515.43 SMI Feynman integral calculus	Next

Includes bibliographical references (pages 305-333) and index.

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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