MU:MU03021 Real Analysis I - Course Information

MU03021 Real Analysis I

Extent and Intensity

2/0/0. 4 credit(s). Type of Completion: zk (examination).

Teacher(s)

doc. RNDr. Michaela Mlíchová, Ph.D. (lecturer)

Guaranteed by

doc. RNDr. Michaela Mlíchová, Ph.D.
Mathematical Institute in Opava

Timetable

Tue 8:05–9:40 RZ

Prerequisites (in Czech)

TYP_STUDIA ( BN )

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

• Mathematical Analysis (programme MU, N1101)
• Mathematics (programme MU, B1101)

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.

• Enrolment Statistics (recent)
  
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