Measure Theory (AN7): Διαφορά μεταξύ των αναθεωρήσεων
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=== General === | === General === |
Τελευταία αναθεώρηση της 16:26, 15 Ιουνίου 2023
- Ελληνική Έκδοση
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General
School | School of Science |
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Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | AN7 |
Semester | 1 |
Course Title | Measure Theory |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | General Background |
Prerequisite Courses | - |
Language of Instruction and Examinations | Language of Instruction (lectures): Greek Language of Instruction (activities other than lectures): Greek and English Language of Examinations: Greek and English |
Is the Course Offered to Erasmus Students | Yes |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes | Using the Bloom Taxonomy. All the following sets are considered to be arbitrary subsets of an arbitrary Euclidean normed space of finite dimension. Remembering:
Comprehension:
Applying:
Evaluating: Teaching undergraduate courses. |
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General Competences |
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Syllabus
Measure spaces, Lebesgue measure, measurable functions and Lebesgue integral, Monotone convergence Theorem and Dominated convergence Theorem, relation between Riemann and Lebesgue integral. Product measures, Fubini Theorem. L^p spaces. Signed measures, Hahn decomposition, Radon-Nikodym Theorem. Convergence of sequences of measurable functions.
Teaching and Learning Methods - Evaluation
Delivery |
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Use of Information and Communications Technology |
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Teaching Methods |
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Student Performance Evaluation |
Language of evaluation: Greek and English.
The aforementioned information along with all the required details are available through the course’s website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course’s website. Upon request, all the information is provided using email or social networks. |
Attached Bibliography
- H.Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011
- L.C. Evans, Partial Differential Equations (2nd ed.). AMS, 2010
- G. Folland, Introduction to Partial Differential Equations, Princeton University Press, 1976
- L. Hörmander, The Analysis of Linear Partial Differential Operators, Vol. 1-4, Springer, 1983-85
- J. Jost, Partial Differential Equations (2nd ed.), Springer, 2007
- T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS, AMS, 2006
- M. Taylor, Partial Differential Equations, Vol. I-III, Springer, 1996
- G.B.Whitham, Linear and Nonlinear Waves, Wiley-Interscience, 1974.