MU24001 Measure Theory and Integration

Mathematical Institute in Opava
Winter 2017
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Michal Málek, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Málek, 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)
Hlavním cílem kurzu je dát studentům teoretický základ pro studium dalších, aplikačně zaměřených předmětů, jako jsou náhodné procesů nebo finanční matematika.
Syllabus
  • Basic properties of measures
    Outer measure and Caratheodory's theorem
    Hausdorff measures
    Lebesgue and Lebegue-Stieltjes measures
    Measurable function as a limits of simple measurable functions
    Sequences of measurable functions
    Integral of a simple measurable function
    Extending the domain of definition of the integral
    Limit theorems for integrals
    Lebesgue-Stieltjes and Lebesgue integrals
    Relationships to Riemann and Henstock-Kurzweil integrals
    Functions of bounded variation and absolutely continuous functions
    - Rotation theory for interval a circle
    (Classical rotation theory of Poincaré, symbolic dynamics)
    - Functional envelopes
    (topological transitivity, chaos, sensitivity to initial conditions)
Literature
    recommended literature
  • M. Misiurewicz. Rotation Theory. URL info
  • S. Kolyada and L. Snoha. Topological transitivity. Scholarpedia, 4(2), 2009. info
  • 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
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2017, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2017/MU24001