# MU:MU03029 Seminar in Real Analysis I - Course Information

## MU03029 Seminar in Real Analysis I

**Mathematical Institute in Opava**

Winter 2016

**Extent and Intensity**- 0/2/0. 4 credit(s). Type of Completion: z (credit).
**Teacher(s)**- doc. RNDr. Michaela Mlíchová, Ph.D. (seminar tutor)
**Guaranteed by**- doc. RNDr. Marta Štefánková, Ph.D.

Mathematical Institute in Opava **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- Mathematical Analysis (programme MU, M1101)
- Mathematics (programme MU, B1101)

**Course objectives**- The scope and content of the seminar is above all curriculum of the course of Real Analysis I. The course serves for the practical exercises and the deepening of student knowledge. Emphasis is placed on autonomous student work.
**Syllabus**- 1. Measures

- Definitions and basic properties

- Outer measure

- Carathéodory's theorem

- Hausdorff measure

- Lebesgue-Stieltjes measure

2. Measurable functions

- Definitions and basic properties

- Approximation of measurable function by simple measurable functions

- Sequences of measurable functions

3. Integration

- Definitions and basic properties

- Limit properties of integrals

- Lebesgue and Lebesgue-Stieljes integral

- 1. Measures
**Literature****Language of instruction**- Czech
**Further comments (probably available only in Czech)**- The course can also be completed outside the examination period.
**Teacher's information**- Active participation in tutorials and handover of solved homework.

- Enrolment Statistics (Winter 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2016/MU03029