Geometry of Sets and Measures in Euclidean Spaces

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.

First sentence: In this chapter we shall introduce some general measure-theoretic concepts, terminology, and results which will be needed later on.

Year

1995

Language

English

Publisher

Cambridge University Press

Editions

2

Pages

356

ISBN

9780521655958

Data source: Wikidata