| Course title | Measure and Integral |
|---|---|
| Course code | KMA/MIM |
| Organizational form of instruction | Lecture + Exercise |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Winter |
| Number of ECTS credits | 6 |
| Language of instruction | Czech |
| Status of course | Compulsory, Compulsory-optional, Optional |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Lecturer(s) |
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| Course content |
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1. Definition of measure and sigma-algebras. 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. Radon-Nikodym derivative. 11. The Fubini theorem.
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| Learning activities and teaching methods |
Lecture, Demonstration
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| Learning outcomes |
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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 |
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Differential and integral calculus of the functions of several variables.
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| Assessment methods and criteria |
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Oral exam
Credit: active participation during seminars. Exam: the student has to understand the subject and be able to prove all theorems. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Data Science (2020) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Mathematics (2020) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics (2023) | Category: Mathematics courses | 1 | Recommended year of study:1, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): General Physics and Mathematical Physics (2019) | Category: Physics courses | 2 | Recommended year of study:2, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Industrial Mathematics (2020) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Winter |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics - Specialization in Business Mathematics (2021) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Winter |