Integral, Probability, and Fractal Measures
Integral, Probability, and Fractal Measures

Author: Gerald A. Edgar

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 292

ISBN-13: 1475729588

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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.

Fractals in Probability and Analysis
Fractals in Probability and Analysis

Author: Christopher J. Bishop

Publisher: Cambridge University Press

Published: 2017

Total Pages: 415

ISBN-13: 1107134110

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A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

The Geometry of Fractal Sets
The Geometry of Fractal Sets

Author: K. J. Falconer

Publisher: Cambridge University Press

Published: 1985

Total Pages: 184

ISBN-13: 9780521337052

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A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.

Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot
Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot

Author: Michel Laurent Lapidus

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 592

ISBN-13: 0821836382

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This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.

Fractal Geometry and Stochastics II
Fractal Geometry and Stochastics II

Author: Christoph Bandt

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 286

ISBN-13: 3034883803

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A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.

Measure, Topology, and Fractal Geometry
Measure, Topology, and Fractal Geometry

Author: Gerald Edgar

Publisher: Springer Science & Business Media

Published: 2007-10-23

Total Pages: 293

ISBN-13: 0387747494

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Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

Fractals
Fractals

Author: G. Cherbit

Publisher:

Published: 1991-01-31

Total Pages: 280

ISBN-13:

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This text will be a valuable tool and reference work for all those interested in fractal forms and their properties. The past decade has seen an almost exponential amount of work done in the field of non-integral dimensions. Upon publication of Mandelbrot's Objets Fractals (1975), a great number of researchers understood the interest of fractals. Many tried, by means of the theory, to set up immediately useable tools, including the author, who opted for an experimental approach and developed instrumentation to explore the widest possible range in both time and space (time resolution of the laser spectroscopy of biomolecules). In this spirit, these expert researchers organized monthly ``Hausdorff seminars on the notion of non-integral dimension and its applications'' to tackle the problems confronting practical scientists. This work captures, with many illustrative examples, the main themes of each session.

Measure Theory
Measure Theory

Author: Vladimir I. Bogachev

Publisher: Springer Science & Business Media

Published: 2007-01-15

Total Pages: 1075

ISBN-13: 3540345140

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This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.

A User-Friendly Introduction to Lebesgue Measure and Integration
A User-Friendly Introduction to Lebesgue Measure and Integration

Author: Gail S. Nelson

Publisher: American Mathematical Soc.

Published: 2015-11-09

Total Pages: 233

ISBN-13: 1470421992

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A User-Friendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well. The book starts with the fundamentals of measure theory that are gently approached through the very concrete example of Lebesgue measure. With this approach, Lebesgue integration becomes a natural extension of Riemann integration. Next, -spaces are defined. Then the book turns to a discussion of limits, the basic idea covered in a first analysis course. The book also discusses in detail such questions as: When does a sequence of Lebesgue integrable functions converge to a Lebesgue integrable function? What does that say about the sequence of integrals? Another core idea from a first analysis course is completeness. Are these -spaces complete? What exactly does that mean in this setting? This book concludes with a brief overview of General Measures. An appendix contains suggested projects suitable for end-of-course papers or presentations. The book is written in a very reader-friendly manner, which makes it appropriate for students of varying degrees of preparation, and the only prerequisite is an undergraduate course in Real Analysis.