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Lectures on Analysis on Metric Spaces

2001 Mathematics
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Release : 2001
Genre : Mathematics
Kind : eBook
Book Rating : 041/5 ( reviews)

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Book Synopsis Lectures on Analysis on Metric Spaces by : Juha Heinonen

Download or read book Lectures on Analysis on Metric Spaces written by Juha Heinonen. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to communicate some of the recent advances in this field while preparing the reader for more advanced study. The material can be roughly divided into three different types: classical, standard but sometimes with a new twist, and recent. The author first studies basic covering theorems and their applications to analysis in metric measure spaces. This is followed by a discussion on Sobolev spaces emphasizing principles that are valid in larger contexts. The last few sections of the book present a basic theory of quasisymmetric maps between metric spaces. Much of the material is recent and appears for the first time in book format.

Introduction to the Analysis of Metric Spaces

1987-09-03 Mathematics
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Release : 1987-09-03
Genre : Mathematics
Kind : eBook
Book Rating : 283/5 ( reviews)

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Book Synopsis Introduction to the Analysis of Metric Spaces by : John R. Giles

Download or read book Introduction to the Analysis of Metric Spaces written by John R. Giles. This book was released on 1987-09-03. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the analysis of metric and normed linear spaces for undergraduate students in mathematics. Assuming a basic knowledge of real analysis and linear algebra, the student is exposed to the axiomatic method in analysis and is shown its power in exploiting the structure of fundamental analysis, which underlies a variety of applications. An example is the link between normed linear spaces and linear algebra; finite dimensional spaces are discussed early. The treatment progresses from the concrete to the abstract: thus metric spaces are studied in some detail before general topology is begun, though topological properties of metric spaces are explored in the book. Graded exercises are provided at the end of each section; in each set the earlier exercises are designed to assist in the detection of the structural properties in concrete examples while the later ones are more conceptually sophisticated.

Metric Spaces And Related Analysis

2023-10-16 Mathematics
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Release : 2023-10-16
Genre : Mathematics
Kind : eBook
Book Rating : 938/5 ( reviews)

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Book Synopsis Metric Spaces And Related Analysis by : Subiman Kundu

Download or read book Metric Spaces And Related Analysis written by Subiman Kundu. This book was released on 2023-10-16. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the comprehensive study of one of the foundational topics in Mathematics, known as Metric Spaces. The book delivers the concepts in an appropriate and concise manner, at the same time rich in illustrations and exercise problems. Special focus has been laid on important theorems like Baire's Category theorem, Heine-Borel theorem, Ascoli-Arzela Theorem, etc, which play a crucial role in the study of metric spaces.The additional chapter on Cofinal completeness, UC spaces and finite chainability makes the text unique of its kind. This helps the students in: Readers will also find brief discussions on various subtleties of continuity like subcontinuity, upper semi-continuity, lower semi-continuity, etc. The interested readers will be motivated to explore the special classes of functions between metric spaces to further extent.Consequently, the book becomes a complete package: it makes the foundational pillars strong and develops the interest of students to pursue research in metric spaces. The book is useful for third and fourth year undergraduate students and it is also helpful for graduate students and researchers.

Topics on Analysis in Metric Spaces

2004 Mathematics
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Release : 2004
Genre : Mathematics
Kind : eBook
Book Rating : 385/5 ( reviews)

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Book Synopsis Topics on Analysis in Metric Spaces by : Luigi Ambrosio

Download or read book Topics on Analysis in Metric Spaces written by Luigi Ambrosio. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on general metric spaces and as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using the 'cavalieri' formula as the definition of the integral. Based on lecture notes from Scuola Normale, this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

Geometry and Analysis of Metric Spaces via Weighted Partitions

2020-11-16 Mathematics
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Release : 2020-11-16
Genre : Mathematics
Kind : eBook
Book Rating : 541/5 ( reviews)

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Book Synopsis Geometry and Analysis of Metric Spaces via Weighted Partitions by : Jun Kigami

Download or read book Geometry and Analysis of Metric Spaces via Weighted Partitions written by Jun Kigami. This book was released on 2020-11-16. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.

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