Course title  Real Analysis I 

Course code  MU/03028 
Organizational form of instruction  Lecture 
Level of course  Master 
Year of study  not specified 
Semester  Winter 
Number of ECTS credits  4 
Language of instruction  Czech 
Status of course  Compulsory, Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


Course content 
Basic properties of measures Outer measure and Caratheodory's theorem Theorem on extension of a measure Measures on metric spaces Hausdorff measure LebesgueStieltjes measure Measurable functions Measurable functions as limits of simple measurable functions Sequences of measurable functions Integrals of simple measurable functions Extending the domain of definition of the integral Limit theorems for integrals Lebesgue and LebesgueStieltjes integrals

Learning activities and teaching methods 
unspecified 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Mathematics (2F)  Mathematics courses  3  Winter 
Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  4  Winter 