## Urs Lang: Catalogue data in Spring Semester 2018 |

Name | Prof. Dr. Urs Lang |

Field | Mathematik |

Address | Professur für Mathematik ETH Zürich, HG G 27.3 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 60 11 |

urs.lang@math.ethz.ch | |

URL | http://www.math.ethz.ch/~lang |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-2284-00L | Measure and Integration | 6 credits | 3V + 2U | U. Lang | |

Abstract | Introduction 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 objective | Basic acquaintance with the abstract theory of measure and integration | ||||

Content | Introduction 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 notes | https://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 | ||||

401-3510-18L | Metric Embedding Theorems | 4 credits | 2S | U. Lang | |

Abstract | A 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 / Notice | Basic knowledge in differential geometry and functional analysis | ||||

401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers | |

Abstract | Research colloquium | ||||

Learning objective | |||||

406-2284-AAL | Measure and IntegrationEnrolment 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 credits | 13R | U. Lang | |

Abstract | Introduction 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 objective | Basic acquaintance with the abstract theory of measure and integration | ||||

Content | |||||

Lecture notes | no lecture notes | ||||

Literature | 1. 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 / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |