Course: Real Analysis I

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Course title Real Analysis I
Course code MU/03028
Organizational form of instruction Lecture
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 4
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.
Course content
Basic properties of measures Outer measure and Caratheodory's theorem Theorem on extension of a measure Measures on metric spaces Hausdorff measure Lebesgue-Stieltjes measure Measurable functions Measurable functions as limits of simple measurable functions Sequences of measurable functions Integrals of simple measurable functions Extending the domain of definition of the integral Limit theorems for integrals Lebesgue and Lebesgue-Stieltjes integrals

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 (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Winter