1	Course Title:	MEASURE THEORY
2	Course Code:	MAT4050
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	8
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	none
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. OSMAN BİZİM
16	Course Lecturers:	Prof. Dr. Osman Bizim
17	Contactinformation of the Course Coordinator:	Uludağ Üniversitesi Fen-Edebiyat Fakültesi Matematik Bölümü, Görükle Bursa-TÜRKİYE 0 224 294 17 50 / obizim@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim and goals of the course are extend the space of Riemann integrable functions and introduce the measure concept that include the concepts the length in R and the area in R2, the volume in R3.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Learns measure, measure function, probability measure, measure space.; 2 Learns outer measure and the Lebesque outer measure.; 3 Learns measurable sets and the measurable functions and their properties.; 4 Learns integrals of simple functions.; 5 Learns the monotone convergence theorem and its properties.;

22	Course Content:

Week	Theoretical	Practical
1	Rings of sets, algebras and algebras of sets, Boole algebras
2	Measure, measure space, measurable space and its examples, measure function.
3	Outer measure, Lebesque outer measure
4	The measurable sets, Lebesque measure, nonmeasurable sets
5	The measurable functions and their properties
6	The Riemann integral and its properties and simple functions.
7	The Lebesgue integral of simple functions and their properties.
8	The Lebesgue integral of nonnegative functions and their properties
9	The monotone convergence theorem and its applications.
10	The Lebesgue integrals of any measurable functions and their properties
11	The Lebesgue convergence theorem and its applications
12	The Lebesgue integral and comparation with the Riemann integral
13	Uniform integral and the Vitali convergence theorem
14	The convergence theorem in measure and its properties

23	Textbooks, References and/or Other Materials:	[1] Real Analysis, H.L.Roydan , I.B. Fitzpatrick [2] Measure Theory, K.B.Athreya, S.N.Lahiri [3] Generalzed Measure Theory, Z.Wang, G.J.Klin
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	4	56
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	21	21
Others	14	2	28
Final Exams	1	31	31
Total WorkLoad			178
Total workload/ 30 hr			5,93
ECTS Credit of the Course			6

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 5 5 5 5 5 5 5 5 5 5 LO2 5 5 5 5 5 5 5 5 5 5 LO3 5 5 5 5 5 5 5 5 5 5 LO4 5 5 5 5 5 5 5 5 5 5 LO5 5 5 5 5 5 5 5 5 5 5

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High