Theory of the Functions of a Real Variable
space
Course code
MLM7006.DT
old course code
MLM7006
Course title in Estonian
Reaalmuutuja funktsioonide teooria
Course title in English
Theory of the Functions of a Real Variable
ECTS credits
6.0
Assessment form
Examination
lecturer of 2023/2024 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2024/2025 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
The course gives students the deeper knowledge in the theory of functions. A student gets acquainted with the notions of Lebesgue measure and Lebesgue integral and their properties, and can compare them with Jordan measure and Riemann integral.
Brief description of the course
Countable sets. Power of a set. Sets with cardinality of the continuum. Comparison of powers. Metric space. Open and closed sets, their structure on the real axis. Perfect sets. Lebesgue measure of a set on the real axis, its properties and comparison with Jordan measure. Measurable functions. Lebegue integral, its properties and comparison with Riemann integral. Spaces of functions integrable in the sense of Lebesgue.
Learning outcomes in the course
Upon completing the course the student:
Student knows mathematical facts and is able to use methods in volume of the subject.
Teacher
prof Anne Tali
space