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Fractal Geometry: Mathematical Foundations and Applications by Kenneth Falconer  (5)
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Product Description
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.
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.
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Inside This Book Citations: This book cites 42 books | 7 books that cite this book Explore: Citations | Books on Related Topics | Concordance | Text Stats Key Phrases - SIPs: metric outer measure, packing measure, divider dimension, open set condition, iterated function system (more) Key Phrases - CAPs: Monotone Convergence Theorem, Strong Law of Large Numbers, Dominated Convergence Theorem, Borel Cantelli Lemma, Fatou's Lemma (more) Browse Sample Pages: Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover | Surprise Me! |
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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!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Copyright | Table of Contents | Excerpt |
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 | Copyright | Table of Contents | Excerpt |