Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

Person Responsible for Information Package

Prof. Adnan MELEKOĞLU

Prof. Hülya İNCEBOZ

Prof. İnci EGE

Prof. Semra DOĞRUÖZ

Assoc. Prof. Berna ARSLAN

Assoc. Prof. Emrah YILDIRIM

Assoc. Prof. Korhan GÜNEL

Ins. Nihal GÜNEL

Lec. Ahmet GENÇ

Lec. Dilek AÇIKGÖZ KAYA

Lec. Erdal ÖZYURT

Lec. Muhammet Ali OKUR

Lec. Okan ARSLAN

Lec. Rıfat AŞLIYAN

Lec. Sibel KOÇER

Res. Assist. İclal GÖR

Res. Assist. Mehmet Soner PEHLİVAN

Measure Theory

Course Code	: MAT418
Course Type	: Area Elective
Couse Group	: First Cycle (Bachelor's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 2
Prt.	: 2
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 use the concepts of set algebra and convergence of set sequences.
2.	Ability to define some set classes such as rings and algebras and to use their relations
3.	Ability to define measurable set
4.	Ability to give the concept of measurement space and its properties.
5.	Ability to use the concepts of outer measure, Lebesque outer measure and Lebesque measure.
6.	Ability to defin some properties of measurable functions
7.	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 & Practice

Course introduction, Concepts of sets, infimum, supremum

Week 2 - Theoretical & Practice

Functions, arrays, set array

Week 3 - Theoretical & Practice

Algebra, ring, ?-algebra

Week 4 - Theoretical & Practice

Borel algebra

Week 5 - Theoretical & Practice

Measurable sets

Week 6 - Theoretical & Practice

Outer measure

Week 7 - Theoretical & Practice

Outer measure

Week 8 - Theoretical & Practice

Measurable according to external size

Week 9 - Theoretical & Practice

Measurable functions

Week 10 - Theoretical & Practice

Borel measurable functions, Lebesque measurable functions

Week 11 - Theoretical & Practice

Theorems about measurable functions

Week 12 - Theoretical & Practice

Integral of simple functions, integral of positive functions

Week 13 - Theoretical & Practice

Reimann integral, Lebesque integral

Week 14 - Theoretical & Practice

Relationship between Reimann integral and Lebesque integral

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	1	%4
Term Assignment	1	%6
Midterm Examination	1	%30
Final Examination	1	%60

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	3	3	84
Assignment	1	1	1	2
Term Project	1	2	1	3
Midterm Examination	1	28	2	30
Final Examination	1	32	2	34
TOTAL WORKLOAD (hours)				153

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		3		5		2		3	2	1	2
OÇ-2	4		4		5		2		3	2	1	2
OÇ-3	4		4		5		2		3	2	1	2
OÇ-4	4		4		5		2		3	2	1	2
OÇ-5	4		4		5		2		3	2	1	2
OÇ-6	4		4		5		2		3	2	1	2
OÇ-7	4		4		5		2		3	2	1	2