The focus of this book is 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 for the subject and develops all the main tools used in its study, 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 Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of Euclidean space possessing many of the properties of smooth surfaces.
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"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.
Book Description
The main theme of this book is the study of geometric properties of general sets and measures in euc lidean space. Examples to which this theory applies 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 for the subject and develops all the main tools used in its study, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. Thus the book is essentially self-contained for graduate students in mathematics; it is primarily targetted at them and researchers.The last third of the book is devoted to the Besicovitch-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space possessing many of the properties of smooth surfaces. These sets have wide application; for example they are central in the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied.
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Inside This Book
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In this chapter we shall introduce some general measure-theoretic concepts, terminology, and results which will be needed later on. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
uniform rectifiability, zero analytic capacity, tangent measures, porous sets, approximate tangent planes, packing measure, rectifiable sets, open set condition, weak type inequality, covering theorem, dyadic cubes, distributed measures, fractal measures, harmonic measure, geometric measure theory, rectifiable curve, density theorem, approximate identity, measurable subset, exceptional set, random measures, singular integrals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem, Using Fatou New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we shall introduce some general measure-theoretic concepts, terminology, and results which will be needed later on. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
uniform rectifiability, zero analytic capacity, tangent measures, porous sets, approximate tangent planes, packing measure, rectifiable sets, open set condition, weak type inequality, covering theorem, dyadic cubes, distributed measures, fractal measures, harmonic measure, geometric measure theory, rectifiable curve, density theorem, approximate identity, measurable subset, exceptional set, random measures, singular integrals Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem, Using Fatou New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
See all 10 books this book cites
2
books
cite this book:
- Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Books on Mathematics) by Juha Heinonen in Back Matter
- The Fractal Geometry of Nature by Benoit B. Mandelbrot in Back Matter
- Measure Theory (Graduate Texts in Mathematics) (v. 18) by Paul R. Halmos in Back Matter
- Selected Problems on Exceptional Sets by L. Carleson in Back Matter
- European Conference on Iteration Theory (Ecit 87 Caldes De Malavella, Spain 20 26 September 1987) by C. Alsian in Back Matter
See all 10 books this book cites
- Integral, Probability, and Fractal Measures by Gerald A. Edgar in Back Matter
- Fractals and Chaos: An illustrated course by Paul S. Addison in Back Matter
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