Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Measure theory and integrals (17.0M515)

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 2, Semester: Winter)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
ECTS	4

Training students for abstract reasoning and acquiring basic knowledge in the field of measure theory and integrals.

The acquired knowledge is used in further education and professional education, mathematical modeling using the results and methodology of measure and integral theory.

Classes of sets. Measurability. Lebesgue external measure. Extension of measures. Lebesgue-Stieltjes measures. Measurable functions. Measures and convergence. Lebesgue integral. Integration of non-measurable functions. Lebesgue limit theorems. Lp-spaces. Decomposition theorems. Duality. Product of measures and integrals.

Lectures; Exercises; Consultations. In the lectures, the theoretical part of the material is presented accompanied by characteristic examples for easier understanding of the material. The exercises follow the lectures used for assignments and expand the material presented in the lectures. In addition to lectures and exercises, consultations are held regularly (one class per week). It is possible to take the exam through two colloquiums. Part of the material that makes up a logical unit can be taken in the form of partial exam obligations that are an integral part of the exam. Partial parts of the exam obligations are taken in written form. The oral part of the final exam as well as the practical part are eliminatory. The condition for listening and taking the exam is passed the exam from Elements of Topology (or a recognized relevant subject).