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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0 of 2 people found the following review helpful:
4.0 out of 5 stars
Seems to be an unread classic,
By R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Integral, Probability, and Fractal Measures (Hardcover)
Some people might prefer an easy approach to fractals,
but long experience has taught me that Dr. Edgar is right in trying to develop fractals in a systematic way. This book tries to lay a foundation in traditional analysis, measure theory and topology for the rough self-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 concrete generating function in complete analysis? Combinatorial theory seems to be a bridge between analysis and fractal measures and that is ignored in this book. The quantum mechanical connection of fractals is also a more recent development, but is shadowed in the product spaces herein.
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Inside This Book
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First Sentence:
We will begin with a review of some measure theory, with an eye to the most common measures used in the study of fractals: the Hausdorff measures and the packing measures. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
metric outer measure, packing measure, divider dimension, open set condition, iterated function system, narrow topology, lambda system, similarity dimension, packing dimension, pointwise dimension, ratio list, fractal measures, complementary intervals, fine cover, covering measure, measurable rectangles, diameter system, countable cover, countable subadditivity, stochastic basis, ultrametric spaces, chaos game, random real number, multifractal formalism, fractal functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monotone Convergence Theorem, Strong Law of Large Numbers, Dominated Convergence Theorem, Borel Cantelli Lemma, Fatou's Lemma, Limit Theorems, Pi-Lambda Theorem, Weierstrass Approximation Theorem, Borel-Cantelli Lemma, Increasing Sets Lemma, Vitali Covering Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We will begin with a review of some measure theory, with an eye to the most common measures used in the study of fractals: the Hausdorff measures and the packing measures. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
metric outer measure, packing measure, divider dimension, open set condition, iterated function system, narrow topology, lambda system, similarity dimension, packing dimension, pointwise dimension, ratio list, fractal measures, complementary intervals, fine cover, covering measure, measurable rectangles, diameter system, countable cover, countable subadditivity, stochastic basis, ultrametric spaces, chaos game, random real number, multifractal formalism, fractal functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monotone Convergence Theorem, Strong Law of Large Numbers, Dominated Convergence Theorem, Borel Cantelli Lemma, Fatou's Lemma, Limit Theorems, Pi-Lambda Theorem, Weierstrass Approximation Theorem, Borel-Cantelli Lemma, Increasing Sets Lemma, Vitali Covering Theorem 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 42
books:
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7
books
cite this book:
See all 7 books citing this book
- Stopping Times and Directed Processes (Encyclopedia of Mathematics and its Applications) by G. A. Edgar in Back Matter
- Classics On Fractals (Studies in Nonlinearity) by Gerald A. Edgar in Back Matter
- Dimension Theory (Princeton Mathematical Ser.; Vol 4) by Witold Hurewicz in Back Matter
- An Eye For Fractals: A Graphic And Photographic Essay (Studies in Nonlinearity) by Michael Mcguire in Back Matter
- The Geometry of Fractal Sets (Cambridge Tracts in Mathematics) by K. J. Falconer in Back Matter
See all 42 books this book cites
- Fractal Concepts in Condensed Matter Physics (Springer Series in Solid-State Sciences) (v. 140) by Tsuneyoshi Nakayama in Back Matter
- Stochastic Calculus and Financial Applications by J. Michael Steele in Back Matter
- Complexus Mundi: Emergent Patterns in Nature by Miroslav M. Novak on page 112
- SuperFractals by Michael Fielding Barnsley in Back Matter
- Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer in Back Matter
See all 7 books citing this book
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