Hausdorff Measures
DOWNLOAD
Download Hausdorff Measures PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Hausdorff Measures book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Hausdorff Measures
DOWNLOAD
Author : Claude Ambrose Rogers
language : en
Publisher: Cambridge University Press
Release Date : 1998-10-22
Hausdorff Measures written by Claude Ambrose Rogers 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 1998-10-22 with Mathematics categories.
When it was first published this was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. There are three chapters: the first contains an introduction to measure theory, paying particular attention to the study of non-s-finite measures. The second develops the most general aspects of the theory of Hausdorff measures, and the third gives a general survey of applications of Hausdorff measures followed by detailed accounts of two special applications. This edition has a foreword by Kenneth Falconer outlining the developments in measure theory since this book first appeared. Based on lectures given by the author at University College London, this book is ideal for graduate mathematicians with no previous knowledge of the subject, but experts in the field will also want a copy for their shelves.
Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff S Ideas
DOWNLOAD
Author : Janusz Czyz
language : en
Publisher: World Scientific
Release Date : 1994-01-14
Paradoxes Of Measures And Dimensions Originating In Felix Hausdorff S Ideas written by Janusz Czyz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-14 with categories.
In this book, many ideas by Felix Hausdorff are described and contemporary mathematical theories stemming from them are sketched. Contents:The Paradox of the SphereInaccessible Numbers and the Hierarchal Structure of Set TheoryThe Hausdorff Measures, Hausdorff Dimensions and FractalsThe Baker-Campbell-Hausdorff FormulaHausdorff MatricesAppendixReferences Readership: Mathematicians, logicians and mathematical physicists. Keywords:Banach-Tarski Paradox;Inaccessible Cardinals;Large Cardinals;Hausdorff Dimension;Fractal;Baker-Campbell-Hausdorff Formula;Lie Superalgebra;Lie Supergroup;Hausdorfd Matrix;Hausdorff Summation;Young-Hausdorff InequalityReview: “Each chapter concludes with an extensive bibliography on the subject. The book should be accessible to mathematicians, pure and applied, as well as to theoretical physicists.” Mathematics Abstracts
Hausdorff Measures Capacities And Sobolev Spaces With Weights
DOWNLOAD
Author : Esko Nieminen
language : en
Publisher:
Release Date : 1991
Hausdorff Measures Capacities And Sobolev Spaces With Weights written by Esko Nieminen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Function spaces categories.
Hausdorff Measures
DOWNLOAD
Author : Claude Ambrose Rogers
language : en
Publisher: Cambridge University Press
Release Date : 1970
Hausdorff Measures written by Claude Ambrose Rogers 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 1970 with Hausdorff measures categories.
Self Similar And Self Affine Sets And Measures
DOWNLOAD
Author : Balázs Bárány
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-16
Self Similar And Self Affine Sets And Measures written by Balázs Bárány and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-16 with Mathematics categories.
Although there is no precise definition of a “fractal”, it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic class of fractal objects. The book contains both introductory material for beginners and more advanced topics, which continue to be the focus of active research. Among the latter are self-similar sets and measures with overlaps, including the much-studied infinite Bernoulli convolutions. Self-affine systems pose additional challenges; their study is often based on ergodic theory and dynamical systems methods. In the last twenty years there have been many breakthroughs in these fields, and our aim is to give introduction to some of them, often in the simplest nontrivial cases. The book is intended for a wide audience of mathematicians interested in fractal geometry, including students. Parts of the book can be used for graduate and even advanced undergraduate courses.
Measure Theoretic Laws For Lim Sup Sets
DOWNLOAD
Author : Victor Beresnevich
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Measure Theoretic Laws For Lim Sup Sets written by Victor Beresnevich 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 2006 with Diophantine approximation categories.
Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\p$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarník concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantineapproximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarník's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarník's theorem opens up the Duffin-Schaeffer conjecturefor Hausdorff measures.
Upper Density Properties Of Hausdorff Measures On Fractals
DOWNLOAD
Author : Arto Salli
language : en
Publisher:
Release Date : 1985
Upper Density Properties Of Hausdorff Measures On Fractals written by Arto Salli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Fractals categories.
Fourier Analysis And Hausdorff Dimension
DOWNLOAD
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.
Advanced Basics Of Geometric Measure Theory
DOWNLOAD
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.
Distance Expanding Random Mappings Thermodynamical Formalism Gibbs Measures And Fractal Geometry
DOWNLOAD
Author : Volker Mayer
language : en
Publisher: Springer
Release Date : 2011-10-25
Distance Expanding Random Mappings Thermodynamical Formalism Gibbs Measures And Fractal Geometry written by Volker Mayer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-25 with Mathematics categories.
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.