Mathematics and Theoretical Computer

By: Gerald A Edgar

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Hardcover | 5 December 1997

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Hardcover
300 Pages

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23.39 x 15.6 x 1.75

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Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.

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Preface
Fractal Measures
Measure Theory	p. 1
Hausdorff and Packing Measures	p. 13
Vitali Theorems	p. 21
Other Local Fractal Measures	p. 28
Geometry of Fractals	p. 41
Ultrametric Spaces	p. 54
Comparable Net Measures	p. 58
Remarks	p. 63
Integrals
Product Measures	p. 69
Integrals	p. 77
Radon-Nikodym Theorem	p. 88
Measures as Linear Functionals	p. 93
Spaces of Measures	p. 100
Remarks	p. 110
Integrals and Fractals
Topological and Fractal Dimension	p. 113
Potential Theory	p. 115
Fractal Measures	p. 123
Self-Affine Graphs	p. 135
Graph Self-Similar Measure	p. 146
Remarks	p. 148
Probability
Events	p. 153
Random Variables	p. 258
Dependence	p. 175
Limit Theorems	p. 195
Remarks	p. 201
Probability and Fractals
The Chaos Game	p. 203
Dimension of Self-Similar Measures	p. 208
Random Cantor Sets	p. 213
Statistical Self-Similarity	p. 220
Statistically Self-Affine Graphs	p. 230
Brownian Motion	p. 249
A Multifractal Decomposition	p. 257
Remarks	p. 262
References	p. 267
Notation	p. 279
Index	p. 281
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Theoretical Computer

At a Glance

Hardcover

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How to return your order

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