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Measure, Topology, and Fractal Geometry Book

Measure, Topology, and Fractal Geometry
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Measure, Topology, and Fractal Geometry, For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so , Measure, Topology, and Fractal Geometry
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  • Measure, Topology, and Fractal Geometry
  • Written by author Gerald Edgar
  • Published by Springer-Verlag New York, LLC, 11/23/2010
  • For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so
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Book Categories

Authors

Fractal Examples     1
The Triadic Cantor Dust     1
The Sierpinski Gasket     7
A Space of Strings     11
Turtle Graphics     14
Sets Defined Recursively     18
Number Systems     31
Remarks     35
Metric Topology     41
Metric Space     41
Metric Structures     48
Separable and Compact Spaces     57
Uniform Convergence     65
The Hausdorff Metric     71
Metrics for Strings     75
Remarks     81
Topological Dimension     85
Zero-Dimensional Spaces     85
Covering Dimension     91
Two-Dimensional Euclidean Space     99
Inductive Dimension     104
Remarks     113
Self-Similarity     117
Ratio Lists     117
String Models     122
Graph Self-Similarity     125
Remarks     133
Measure Theory     137
Lebesgue Measure     137
Method I     146
Two-Dimensional Lebesgue Measure     152
Metric Outer Measure     155
Measuresfor Strings     159
Remarks     162
Fractal Dimension     165
Hausdorff Measure     165
Packing Measure     169
Examples     177
Self-Similarity     185
The Open Set Condition     190
Graph Self-Similarity     199
Graph Open Set Condition     205
Other Fractal Dimensions     210
Remarks     216
Additional Topics     225
Deconstruction     225
Self-Affine Sets     229
Self-Conformal     234
A Multifractal     238
A Superfractal     242
Remarks     247
Appendix     251
Terms     251
Notation     254
Examples     255
Reading     255
References     257
Index     261


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Measure, Topology, and Fractal Geometry, For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so , Measure, Topology, and Fractal Geometry

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Measure, Topology, and Fractal Geometry, For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so , Measure, Topology, and Fractal Geometry

Measure, Topology, and Fractal Geometry

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Measure, Topology, and Fractal Geometry, For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so , Measure, Topology, and Fractal Geometry

Measure, Topology, and Fractal Geometry

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