Topics On Analysis In Metric Spaces

Author : Luigi Ambrosio,Paolo Tilli
Publisher : Oxford University Press, USA
Page : 148 pages
File Size : 54,5 Mb
Release : 2004
Category : Mathematics
ISBN : 0198529384

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Topics on Analysis in Metric Spaces by Luigi Ambrosio,Paolo Tilli Pdf

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.

Author : Juha Heinonen
Publisher : Springer Science & Business Media
Page : 149 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301318

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Lectures on Analysis on Metric Spaces by Juha Heinonen Pdf

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.

Author : Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam
Publisher : Springer Nature
Page : 312 pages
File Size : 42,5 Mb
Release : 2022-02-04
Category : Mathematics
ISBN : 9783030841416

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New Trends on Analysis and Geometry in Metric Spaces by Fabrice Baudoin,Séverine Rigot,Giuseppe Savaré,Nageswari Shanmugalingam Pdf

This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.

Author : John R. Giles
Publisher : Cambridge University Press
Page : 276 pages
File Size : 44,8 Mb
Release : 1987-09-03
Category : Mathematics
ISBN : 0521359287

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Introduction to the Analysis of Metric Spaces by John R. Giles Pdf

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.

Author : S. Kumaresan
Publisher : Alpha Science Int'l Ltd.
Page : 172 pages
File Size : 55,5 Mb
Release : 2005
Category : Computers
ISBN : 1842652508

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Topology of Metric Spaces by S. Kumaresan Pdf

"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.

Author : Joseph Muscat
Publisher : Springer Nature
Page : 462 pages
File Size : 46,9 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031275371

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Functional Analysis by Joseph Muscat Pdf

Author : Luigi Ambrosio,Paolo Tilli
Publisher : Unknown
Page : 133 pages
File Size : 53,5 Mb
Release : 2000
Category : Electronic
ISBN : OCLC:875782909

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Selected topics on analysis in metric spaces by Luigi Ambrosio,Paolo Tilli Pdf

Author : Luigi Ambrosio,Nicola Gigli,Giuseppe Savare
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 54,5 Mb
Release : 2008-10-29
Category : Mathematics
ISBN : 9783764387228

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Gradient Flows by Luigi Ambrosio,Nicola Gigli,Giuseppe Savare Pdf

The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.

Author : Amar Kumar Banerjee
Publisher : New Age International
Page : 27 pages
File Size : 52,6 Mb
Release : 2008
Category : Electronic
ISBN : 9788122422603

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Metric Spaces and Complex Analysis by Amar Kumar Banerjee Pdf

Author : Satish Shirali,Harkrishan Lal Vasudeva
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 50,7 Mb
Release : 2006
Category : Mathematics
ISBN : 1852339225

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Metric Spaces by Satish Shirali,Harkrishan Lal Vasudeva Pdf

One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily

Author : Shou Lin,Ziqiu Yun
Publisher : Springer
Page : 328 pages
File Size : 46,8 Mb
Release : 2016-10-20
Category : Mathematics
ISBN : 9789462392168

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Generalized Metric Spaces and Mappings by Shou Lin,Ziqiu Yun Pdf

The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 420 pages
File Size : 42,7 Mb
Release : 2000-08-15
Category : Mathematics
ISBN : 0521497566

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Real Analysis by N. L. Carothers Pdf

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

Author : Tom L. Lindstrøm
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 44,6 Mb
Release : 2017-11-28
Category : Functional analysis
ISBN : 9781470440626

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Spaces: An Introduction to Real Analysis by Tom L. Lindstrøm Pdf

Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.

Author : Robert Magnus
Publisher : Springer
Page : 244 pages
File Size : 42,5 Mb
Release : 2022-03-17
Category : Mathematics
ISBN : 3030949451

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Metric Spaces by Robert Magnus Pdf

This textbook presents the theory of Metric Spaces necessary for studying analysis beyond one real variable. Rich in examples, exercises and motivation, it provides a careful and clear exposition at a pace appropriate to the material. The book covers the main topics of metric space theory that the student of analysis is likely to need. Starting with an overview defining the principal examples of metric spaces in analysis (chapter 1), it turns to the basic theory (chapter 2) covering open and closed sets, convergence, completeness and continuity (including a treatment of continuous linear mappings). There is also a brief dive into general topology, showing how metric spaces fit into a wider theory. The following chapter is devoted to proving the completeness of the classical spaces. The text then embarks on a study of spaces with important special properties. Compact spaces, separable spaces, complete spaces and connected spaces each have a chapter devoted to them. A particular feature of the book is the occasional excursion into analysis. Examples include the Mazur–Ulam theorem, Picard’s theorem on existence of solutions to ordinary differential equations, and space filling curves. This text will be useful to all undergraduate students of mathematics, especially those who require metric space concepts for topics such as multivariate analysis, differential equations, complex analysis, functional analysis, and topology. It includes a large number of exercises, varying from routine to challenging. The prerequisites are a first course in real analysis of one real variable, an acquaintance with set theory, and some experience with rigorous proofs.

Author : Alexander Kharazishvili
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 50,9 Mb
Release : 2009-11-01
Category : Mathematics
ISBN : 9789491216367

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TOPICS IN MEASURE THEORY AND REAL ANALYSIS by Alexander Kharazishvili Pdf

This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology.