Lecturer(s)


Vodák Rostislav, RNDr. Ph.D.

Pastor Karel, doc. Mgr. Ph.D.

Fürst Tomáš, RNDr. Ph.D.

Vencálek Ondřej, Mgr. Ph.D.

Course content

1. Definition of measure and sigmaalgebras. 2. Basic properties of measures. 3. Outer measure and the Caratheodory extension theorem. 4. The Lebesgue measure. 5. Measurable functions. 6. Sequences of measurable functions and types of convergence. 7. The Lebesgue integral. 8. Properties of the Lebesgue integral. 9. Generalized measures, the Hahn and Jordan decomposition. 10. RadonNikodym derivative. 11. The Fubini theorem.

Learning activities and teaching methods

Lecture, Demonstration
 Attendace
 52 hours per semester
 Homework for Teaching
 45 hours per semester
 Preparation for the Exam
 80 hours per semester

Learning outcomes

Understand the abstract construction of an integral based on a measure.
Comprehension Understand the more abstract construction of an integral based on a measure.

Prerequisites

Differential and integral calculus of the functions of several variables.
KMA/MA2M

Assessment methods and criteria

Oral exam
Credit: active participation during seminars. Exam: the student has to understand the subject and be able to prove all theorems.

Recommended literature


J. Lukeš, J. Malý. (1995). Measure and Intergral. Matfyzpress, Praha.

P. R. Halmos. (1950). Measure theory. New York, D. Van Nostrand Company.

V. Jarník. (1984). Integrální počet (I), (II).. Academia, Praha.
