Urs Lang: Catalogue data in Spring Semester 2018

Name Prof. Dr. Urs Lang
FieldMathematik
Address
Professur für Mathematik
ETH Zürich, HG G 27.3
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 60 11
E-mailurs.lang@math.ethz.ch
URLhttp://www.math.ethz.ch/~lang
DepartmentMathematics
RelationshipFull Professor

NumberTitleECTSHoursLecturers
401-2284-00LMeasure and Integration Information 6 credits3V + 2UU. Lang
AbstractIntroduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Learning objectiveBasic acquaintance with the abstract theory of measure and integration
ContentIntroduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Lecture noteshttps://people.math.ethz.ch/~lang/mi.pdf
Literature- D. A. Salamon, Measure and Integration, EMS 2016
- W. Rudin, Real and Complex Analysis, McGraw-Hill 1987
- P. R. Halmos, Measure Theory, Springer 1950
401-3510-18LMetric Embedding Theorems Restricted registration - show details 4 credits2SU. Lang
AbstractA tour of various (isometric, bi-Lipschitz, coarse, ...) embedding theorems for metric spaces into Banach spaces or other spaces with some extra structure.
Learning objective
Literature- Juha Heinonen, Geometric Embeddings of Metric Spaces, Lecture Notes, 2003, s. https://jyx.jyu.fi/dspace/handle/123456789/22520
- Mikhail I. Ostrovskii, Metric Embeddings: Bilipschitz and Coarse Embeddings into Banach Spaces, De Gruyter 2013
Prerequisites / NoticeBasic knowledge in differential geometry and functional analysis
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers
AbstractResearch colloquium
Learning objective
406-2284-AALMeasure and Integration
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
6 credits13RU. Lang
AbstractIntroduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Learning objectiveBasic acquaintance with the abstract theory of measure and integration
ContentIntroduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
Lecture notesno lecture notes
Literature1. P.R. Halmos, "Measure Theory", Springer
2. Extra material: Lecture Notes by Emmanuel Kowalski and Josef Teichmann from spring semester 2012, http://www.math.ethz.ch/~jteichma/measure-integral_120615.pdf
3. Extra material: P. Cannarsa & T. D'Aprile, "Lecture Notes on Measure Theory and Functional Analysis", http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf
Prerequisites / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.