### Measure Theory

Wednesday and Thursday, 15:15-17:00 in Seminarraum 11 (OMP 1)

**Summary:** The Lebesgue measure and integration
theory is one of the pillars of modern analysis and the
cornerstone of the probability theory. The lecture presents
its basic concepts and results (in particular the existence,
uniqueness and important examples of measures, Lebesgue
integral, convergence theorems, spaces of integrable
functions, product measures) and connects these results with
other areas of mathematics.

**Questions for the exam:** download

**Literature:**

- Amann-Escher: Analysis III. Birkhäuser
- Billingsley: Probability and measure. Wiley
- Cohn: Measure Theory. Birkhäuser
- Evans-Gariepy: Measure theory and fine properties of functions. CRC Press
- Rudin: Real and complex analysis. McGraw-Hill
- Tao: An introduction to measure theory. AMS
- Wheeden-Zygmund: Measure and integral. Dekker.

**Lecture notes:**
handwritten lecture notes

### Proseminar on Measure Theory

Wednesday 13:15-15:00 Seminarraum 8 (OMP1)

**Summary:** The proseminar complements the lecture
with examples, exercises and short talks.

**Problems for solution:**
9 October,
16 October,
23 October,
30 October,
6 November,
13 November,
20 November
(solutions),
27 November
(solutions),
4 December
(solutions),
11 December
(solutions),
18 December - no proseminar,
8 January
(solutions),
15 January
(solutions),
22 January

### Seminar on Probability Theory

Tuesday 17:00-18:30 Seminarraum 12 (OMP1)

For the programm see the page of the seminar