Measure Theory (MAE616): Διαφορά μεταξύ των αναθεωρήσεων
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! Course Website (URL) | ! Course Website (URL) | ||
| | | See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina. | ||
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Αναθεώρηση της 12:35, 13 Αυγούστου 2022
Undergraduate Courses Outlines - Department of Mathematics
General
School |
School of Science |
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Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
MAE616 |
Semester |
6 |
Course Title |
Measure Theory |
Independent Teaching Activities |
Lectures (Weekly Teaching Hours: 3, Credits: 6) |
Course Type |
Special background |
Prerequisite Courses |
None (from the typical point of view). In order to be able to follow this course, the knowledge from the following courses are required: Infinetisimal Calculus I, Introduction to Topology. |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students |
Yes (exams in English are provided for foreign students) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
After completing this course the students will
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General Competences |
The course promotes inductive and creative thinking and aims to provide the student with the theoretical background and skills to use measure theory and integration. |
Syllabus
Algebras, σ-algebras, measures, outer measures, Caratheodory's Theorem (concerning the construction of a measure from an outer measure). Lebesgue measure, definition and properties. Measurable functions. Lebesgue integral, Lebesgue's Monotone Convergernce Theorem, Lebesgue's Dominated Convergence Theorem. Comparison between Riemann integral and Lebesgue integral for functions defined on closed bounded integrals of the set of reals.
Teaching and Learning Methods - Evaluation
Delivery |
Teaching on the blackboard by the teacher. | ||||||||||
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Use of Information and Communications Technology |
Communication with the teacher by electronic means (i.e. e-mail). | ||||||||||
Teaching Methods |
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Student Performance Evaluation |
Exams in the end of the semester (mandatory), potential intermediate exams (optional), assignments of exercises during the semester (optional). |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally:
- Measure Theory, Donald Cohn, Birkhauser.