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- Department of Mathematics
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School of Science
Department of Mathematics
|Level of Studies||
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
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||
|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.|
After completing this course the students will
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.
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
Teaching on the blackboard by the teacher.
|Use of Information and Communications Technology||
Communication with the teacher by electronic means (i.e. e-mail).
|Student Performance Evaluation||
Exams in the end of the semester (mandatory), potential intermediate exams (optional), assignments of exercises during the semester (optional).
- Measure Theory, Donald Cohn, Birkhauser.