Course: Seminar in Real Analysis I

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Course title Seminar in Real Analysis I
Course code MU/03022
Organizational form of instruction Seminary
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 2
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • ŠTEFÁNKOVÁ Marta, doc. RNDr. Ph.D.
  • MLÍCHOVÁ Michaela, RNDr. Ph.D.
Course content
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

Learning activities and teaching methods
unspecified
Recommended literature
  • A. M. Bruckner, J. B. Bruckner, B. S. Thomson. Real Analysis. Upper Saddle River, New Jersey, 1997. ISBN 0-13-458886-X.
  • M. Švec, T. Šalát, T. Neubrunn. Matematická analýza funkcií reálnej premennej. Bratislava, 1987.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 1 Winter