Information Package / Course Catalogue
Measure Theory
Course Code: MAT418
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

This course aims to teach algebras, measurability, measurable sets, The Lebesque-Steieltjes integral

Course Content

Measurement on algebras and sigma algebras, Lebesgue measure on intervals, Internal and external measurements of sets, Measurable sets, Measurable functions, Lebesgue-Stieltjes measure and integrals of functions

Name of Lecturer(s)
Learning Outcomes
1.Ability to define measure on algebras and sigma algebras
2.Ability to define Lebesque measure on intervals
3.Ability to define measurable set
4.To learn some properties of measurable functions
5.Ability to define the Lebesque-Stieltjes integral
Recommended or Required Reading
1.Lebesque integral kuramına giriş, R. Bartle, Matematik Vakfı Yayınları
2.Reel Analiz, Mustafa Balcı, Palme Yayınevi
Weekly Detailed Course Contents
Week 1 - Theoretical
Concepts of sets, infimum, supremum
Week 2 - Theoretical
Functions, arrays, set array
Week 3 - Theoretical
Algebra, ring, ?-algebra
Week 4 - Theoretical
Borel algebra
Week 5 - Theoretical
Measurable sets
Week 6 - Theoretical
Outer measure
Week 7 - Theoretical
Outer measure
Week 8 - Theoretical
Measurable according to external size
Week 9 - Theoretical
Measurable functions
Week 10 - Theoretical
Borel measurable functions, Lebesque measurable functions
Week 11 - Theoretical
Theorems about measurable functions
Week 12 - Theoretical
Integral of simple functions, integral of positive functions
Week 13 - Theoretical
Reimann integral, Lebesque integral
Week 14 - Theoretical
Relationship between Reimann integral and Lebesque integral
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Midterm Examination130232
Final Examination132234
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
4
4
5
2
5
4
2
3
5
OÇ-2
4
4
5
2
5
4
2
3
5
OÇ-3
4
4
5
2
5
4
2
3
5
OÇ-4
4
4
5
2
5
4
2
3
5
OÇ-5
4
4
5
2
5
4
2
3
5
Adnan Menderes University - Information Package / Course Catalogue
2026