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Integral, Probability, and Fractal Measures : Mathematics and Theoretical Computer - Gerald A. Edgar

Integral, Probability, and Fractal Measures

Mathematics and Theoretical Computer

Hardcover Published: 5th December 1997
ISBN: 9780387982052
Number Of Pages: 286

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This book provides the mathematical background required for the study of fractal topics. It deals with integration in the modern sense and with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals. The book follows on Edgar's Measure, Topology, and Fractal Geometry. With exercises throughout the text, it is ideal for beginning graduate students both in the classroom setting and for self-study.

Fractal Measures
Measure Theoryp. 1
Hausdorff and Packing Measuresp. 13
Vitali Theoremsp. 21
Other Local Fractal Measuresp. 28
Geometry of Fractalsp. 41
Ultrametric Spacesp. 54
Comparable Net Measuresp. 58
Remarksp. 63
Product Measuresp. 69
Integralsp. 77
Radon-Nikodym Theoremp. 88
Measures as Linear Functionalsp. 93
Spaces of Measuresp. 100
Remarksp. 110
Integrals and Fractals
Topological and Fractal Dimensionp. 113
Potential Theoryp. 115
Fractal Measuresp. 123
Self-Affine Graphsp. 135
Graph Self-Similar Measurep. 146
Remarksp. 148
Eventsp. 153
Random Variablesp. 258
Dependencep. 175
Limit Theoremsp. 195
Remarksp. 201
Probability and Fractals
The Chaos Gamep. 203
Dimension of Self-Similar Measuresp. 208
Random Cantor Setsp. 213
Statistical Self-Similarityp. 220
Statistically Self-Affine Graphsp. 230
Brownian Motionp. 249
A Multifractal Decompositionp. 257
Remarksp. 262
Referencesp. 267
Notationp. 279
Indexp. 281
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387982052
ISBN-10: 0387982051
Series: Mathematics and Theoretical Computer
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 286
Published: 5th December 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.56