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Measure and integration

Code: 61809
ECTS: 5.0
Lecturers in charge: doc. dr. sc. Rudi Mrazović
doc. dr. sc. Vanja Wagner
Lecturers: Adrian Beker - Exercises
dr. sc. Aleksandar Bulj - Exercises
dr. sc. Martina Stojić Zibar - Exercises
Tadej Petar Tukara - Exercises
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
COURSE AIMS AND OBJECTIVES: To introduce notions of measure, measurable functions and abstract integration, as well as main theorems of measure and integral.

1. introduction. Semirings and rings of sets. Sigma - ring of sets.
2. Finitely and countably additive functions. Measures on rings.
3. Caratheodory construction.
4. Lebesgue measure. Regularity. Measures on reals.
5. Measurable functions. Integral of a simple function.
6. Integral of a nonnegative function. Monotone convergence theorem.
7. Integrable functions. Dominated convergence theorem.
8. Lebesgue Lp - spaces.
9. Hahn and Jordan decomposition of a measure. Absolute continuity. Singularity.
10. Radon - Nikodym theorem. Lebesgue decomposition.
11. Convergence types. Egorov theorem.
12. Product measures. Fubini - Tonelli theorem.
13. Riesz representation theorem of positive linear functionals.
Prerequisit for:
Enrollment :
Passed : Fundamentals of mathematical analysis
Passed : Linear algebra 2
10. semester
Izborni matematički predmet 5 - Regular study - Mathematics and Physics Education
Consultations schedule:


Link to the course web page: https://web.math.pmf.unizg.hr/nastava/mii/