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  3. Geometry of Sets and Measures in Euclidean Spaces
  • Cited by 1333
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    • Publisher:
      Cambridge University Press
      Publication date:
      August 2012
      April 1995
      ISBN:
      9780511623813
      9780521655958
      DOI:
      https://doi.org/10.1017/CBO9780511623813
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.52kg, 356 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      Cambridge Studies in Advanced Mathematics (44)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Cambridge Studies in Advanced Mathematics (44)
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    Book description

    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.

    Reviews

    "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.

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