Geometry Of Sets And Measures In Euclidean Spaces
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Geometry Of Sets And Measures In Euclidean Spaces
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-25
Geometry Of Sets And Measures In Euclidean Spaces written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-25 with Mathematics categories.
This book studies the geometric properties of general sets and measures in euclidean space.
Geometry Of Sets And Measures In Euclidean Spaces
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Author : Pertti Mattila
language : en
Publisher:
Release Date : 1992
Geometry Of Sets And Measures In Euclidean Spaces written by Pertti Mattila and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
The Geometry Of Fractal Sets
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Author : K. J. Falconer
language : en
Publisher: Cambridge University Press
Release Date : 1985
The Geometry Of Fractal Sets written by K. J. Falconer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
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.
Rectifiable Sets Densities And Tangent Measures
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Author : Camillo De Lellis
language : en
Publisher: European Mathematical Society
Release Date : 2008
Rectifiable Sets Densities And Tangent Measures written by Camillo De Lellis and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former and provide some perspective of the latter. This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students; the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in Euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.
Lebesgue Integration On Euclidean Space
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Author : Frank Jones
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2001
Lebesgue Integration On Euclidean Space written by Frank Jones and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
"'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --
Fourier Analysis And Hausdorff Dimension
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-22
Fourier Analysis And Hausdorff Dimension written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-22 with Mathematics categories.
Modern text examining the interplay between measure theory and Fourier analysis.
Finer Thermodynamic Formalism Distance Expanding Maps And Countable State Subshifts Of Finite Type Conformal Gdmss Lasota Yorke Maps And Fractal Geometry
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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-06-06
Finer Thermodynamic Formalism Distance Expanding Maps And Countable State Subshifts Of Finite Type Conformal Gdmss Lasota Yorke Maps And Fractal Geometry written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-06 with Mathematics categories.
This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere.
Measures Integrals And Martingales
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Author : René L. Schilling
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-10
Measures Integrals And Martingales written by René L. Schilling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-10 with Mathematics categories.
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions can be found on the authors website, which can be reached at http: //www.motapa.de/measures_integrals_and_martingales/index.htm
An Introduction To Measure Theory
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-03
An Introduction To Measure Theory written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Education categories.
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Advanced Basics Of Geometric Measure Theory
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Author : Maria Roginskaya
language : en
Publisher: Lulu.com
Release Date : 2015
Advanced Basics Of Geometric Measure Theory written by Maria Roginskaya and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Science categories.
This book is based on lecture notes for a short course for Masters level or senior undergraduate students. It may also serve as easy (and hopefully pleasant) reading for researchers in a different field of Mathematics. The main purpose of the book is to look closely at some results that are basic for modern Analysis and which fascinated the author when she was a student, and to show how they constitute a foundation for the branch of Analysis known as Geometric Measure Theory. The secondary aim of the book is to give a straightforward but reasonably complete introduction to the definition of Hausdorff measure and Hausdorff dimension and to illustrate how non-trivial they can be. The course has no ambition to replace a serious course on Geometric Measure Theory, but rather to encourage the student to take such a course. The author comes from Russia. For the past 17 years she has worked at Chalmers University of Technology in Gothenburg, Sweden. She also had visiting positions in Canada, France, and Poland.