MU03021 Real Analysis I

Mathematical Institute in Opava
Winter 2016
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Marta Štefánková, Ph.D. (lecturer)
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 (in Czech)
Probírá se teorie míry a teorie integrálu.
Syllabus
  • 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
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.
The course is also listed under the following terms Winter 2014, Winter 2015, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021, Winter 2022.
  • Enrolment Statistics (Winter 2016, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2016/MU03021