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
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