MU03028 Real Analysis I

Mathematical Institute in Opava
Winter 2019
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: z (credit).
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 offered to students of any study field.
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)
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1997, Winter 1998, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (recent)
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