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

This book provides a comprehensive and unified foundation for the study of geometric properties of general sets and measures in Euclidean spaces.

With a focus on fractal-type objects, such as strange attractors and models used in the sciences, the author develops all the main tools needed for their analysis, including covering theorems, Hausdorff measures, and their relations to Riesz capacities and Fourier transforms.

The book also explores the Besicovitch-Federer theory of rectifiable sets, which form the largest class of subsets of Euclidean space possessing many properties of smooth surfaces.

This summary highlights the book's emphasis on providing a firm foundation for the subject and its relevance to fractals and dynamical systems, making it an essential resource for researchers and students in mathematics and related fields.