Buch, Englisch, 142 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 385 g
Buch, Englisch, 142 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 385 g
ISBN: 978-0-19-852938-5
Verlag: OUP Oxford
Based on lecture notes from the 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.
The book covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed in a general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed in 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 Cavalieri's formula as the definition of the integral.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
- Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
- Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
- Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke
- Mathematik | Informatik Mathematik Mathematik Allgemein
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
- 1: Some preliminaries in measure theory
- 2: Hausdorff measures and covering theorems in metric spaces
- 3: Lipschitz functions in metric spaces
- 4: Geodesic problem and Gromov-Hausdorff convergence
- 5: Sobolev spaces in a metric framework
- 6: A quick overview on the theory of integration
