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Integral, Probability, and Fractal Measures - Advanced Mathematics & Theoretical Computer Science Textbook | Perfect for Graduate Studies & Research in Mathematical Analysis
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Integral, Probability, and Fractal Measures - Advanced Mathematics & Theoretical Computer Science Textbook | Perfect for Graduate Studies & Research in Mathematical Analysis
Integral, Probability, and Fractal Measures - Advanced Mathematics & Theoretical Computer Science Textbook | Perfect for Graduate Studies & Research in Mathematical Analysis
Integral, Probability, and Fractal Measures - Advanced Mathematics & Theoretical Computer Science Textbook | Perfect for Graduate Studies & Research in Mathematical Analysis
$23.72
$43.13
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Description
This book may be considered a continuation of my Springer-Verlag text Mea­ sure, Topology, and Fractal Geometry. It presupposes some elementary knowl­ edge of fractal geometry and the mathematics behind fractal geometry. Such knowledge might be obtained by study of Measure, Topology, and Fractal Ge­ ometry or by study of one of the other mathematically oriented texts (such as [13] or [87]). I hope this book will be appropriate to mathematics students at the beginning graduate level in the U.S. Most references are numbered and may be found at the end of the book; but Measure, Topology, and Fractal Geometry is referred to as [ MTFG]. One of the reviews of [MTFG] says that it "sacrific[es] breadth of coverage 1 for systematic development" -although I did not have it so clearly formulated as that in my mind at the time I was writing the book, I think that remark is exactly on target. That sacrifice has been made in this volume as well. In many cases, I do not include the most general or most complete form of a result. Sometimes I have only an example of an important development. The goal was to omit most material that is too tedious or that requires too much background.
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5
Some people might prefer an easy approach to fractals,but long experience has taught me that Dr. Edgar is right in trying to develop fractalsin a systematic way. This book tries to lay a foundationin traditional analysis, measure theory and topology for the roughself-similarity of sand piles and drainage basins.The trajectories of Levy flights are shown on page 248,but as in his other books Edgar seems to forget that you need concretegenerating function in complete analysis?Combinatorial theory seems to be a bridge between analysis and fractal measuresand that is ignored in this book. The quantum mechanicalconnection of fractals is also a more recent development,but is shadowed in the product spaces herein.

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