Topics in Real Functions (MAE752)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code




Course Title

Topics on Real Functions

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations


Is the Course Offered to Erasmus Students


Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The plan of the course is the achievement by the undergraduate student of special theoretical background in the theory of real functions.

General Competences

The objective of the course is the undergraduate student's ability achievement in analysis and synthesis of the basic background in the theory of real functions.


Monotone functions-continuity, functions of bounded variation, Fς and Gd sets, sets of measure zero, Lebesgue's theorem (every monotone function is differentiable almost everywhere), Darboux continuous functions-definitions, properties, equivalent characterizations, criteria, Semicontinuous functions, differentiability of the Riemann integral of a function, Baire classes, Borel measurable functions, analytic sets-characterizations, connections with Borel sets-related theory, Lebesgue and Stieltjes integrals.

Teaching and Learning Methods - Evaluation



Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Independent study 78
Exercises solutions 33
Course total 150
Student Performance Evaluation

Written examination at the end of the semester.

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. Books and other resources, not provided by Eudoxus:

  • A.C.M. Van Rooij, W.H. Schikhof, Α second course on real functions, Cambridge University Press.