Topics On Analysis In Metric Spaces
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| Author | : Luigi Ambrosio |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 148 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780198529385 |
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 | : Luigi Ambrosio |
| Publisher | : |
| Total Pages | : 133 |
| Release | : 2000 |
| Genre | : |
| ISBN | : |
| Author | : Juha Heinonen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 158 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780387951041 |
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 | : S. Kumaresan |
| Publisher | : Alpha Science Int'l Ltd. |
| Total Pages | : 172 |
| Release | : 2005 |
| Genre | : Computers |
| ISBN | : 9781842652503 |
"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 | : Fabrice Baudoin |
| Publisher | : Springer Nature |
| Total Pages | : 312 |
| Release | : 2022-02-04 |
| Genre | : Mathematics |
| ISBN | : 3030841413 |
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 |
| Total Pages | : 276 |
| Release | : 1987-09-03 |
| Genre | : Mathematics |
| ISBN | : 9780521359283 |
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 | : Amar Kumar Banerjee |
| Publisher | : New Age International |
| Total Pages | : 27 |
| Release | : 2008 |
| Genre | : |
| ISBN | : 8122422608 |
| Author | : Joseph Muscat |
| Publisher | : Springer Nature |
| Total Pages | : 462 |
| Release | : |
| Genre | : |
| ISBN | : 3031275373 |
| Author | : Robert B. Ash |
| Publisher | : Courier Corporation |
| Total Pages | : 216 |
| Release | : 2014-07-28 |
| Genre | : Mathematics |
| ISBN | : 0486151492 |
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis. The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Detailed solutions to the problems appear within the text, making this volume ideal for independent study. Topics include metric spaces, Euclidean spaces and their basic topological properties, sequences and series of real numbers, continuous functions, differentiation, Riemann-Stieltjes integration, and uniform convergence and applications.
| Author | : Victor Bryant |
| Publisher | : Cambridge University Press |
| Total Pages | : 116 |
| Release | : 1985-05-02 |
| Genre | : Mathematics |
| ISBN | : 9780521318976 |
An introduction to metric spaces for those interested in the applications as well as theory.
