Topics on Analysis in Metric Spaces

Topics on Analysis in Metric Spaces
Author :
Publisher : OUP Oxford
Total Pages : 148
Release :
ISBN-10 : 0198529384
ISBN-13 : 9780198529385
Rating : 4/5 (385 Downloads)

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 and published by OUP Oxford. This book was released on 2004 with total page 148 pages. 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.


Topics on Analysis in Metric Spaces Related Books

Topics on Analysis in Metric Spaces
Language: en
Pages: 148
Authors: Luigi Ambrosio
Categories: Mathematics
Type: BOOK - Published: 2004 - Publisher: OUP Oxford

GET EBOOK

This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions
Lectures on Analysis on Metric Spaces
Language: en
Pages: 149
Authors: Juha Heinonen
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important
Descriptive Topology in Selected Topics of Functional Analysis
Language: en
Pages: 494
Authors: Jerzy Kąkol
Categories: Mathematics
Type: BOOK - Published: 2011-08-30 - Publisher: Springer Science & Business Media

GET EBOOK

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focus
Metric Spaces
Language: en
Pages: 318
Authors: Mícheál O'Searcoid
Categories: Mathematics
Type: BOOK - Published: 2006-12-26 - Publisher: Springer Science & Business Media

GET EBOOK

The abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of
Introduction to the Analysis of Metric Spaces
Language: en
Pages: 276
Authors: John R. Giles
Categories: Mathematics
Type: BOOK - Published: 1987-09-03 - Publisher: Cambridge University Press

GET EBOOK

Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the pow