MU03022 Seminar in Real Analysis I

Mathematical Institute in Opava
Winter 2018
Extent and Intensity
0/2/0. 2 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
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
Literature
    recommended literature
  • A. M. Bruckner, J. B. Bruckner, B. S. Thomson. Real Analysis. Upper Saddle River, New Jersey, 1997. ISBN 0-13-458886-X. info
  • M. Švec, T. Šalát, T. Neubrunn. Matematická analýza funkcií reálnej premennej. Bratislava, 1987. info
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.
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2019, Winter 2020, Winter 2021.
  • Enrolment Statistics (Winter 2018, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2018/MU03022