Yozgat Bozok University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT509	MEASURE THEORY	Elective	1	2	6

Level of Course Unit

Second Cycle

Objectives of the Course

To introduce to the student concept of Lebesgue integral, and applications.

Name of Lecturer(s)

Doç. Dr. Abdullah SÖNMEZOĞLU

Learning Outcomes

1	To prove theorems about measurable sets and measurable functions
2	Identify and apply the concept of Lebesgue integral
3	To learn the relationship between Lebesgue integral and Riemann integral

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Sigma Algebra and Algebra Concepts, Axiom of Choice and the Infinite Direct Products, Countable Sets Real Number System, Open and Closed Sets, Borel Sets Measurement and Measurement Concepts International Measurable sets and Lebesgue Measure Clusters can not be measured Measurement concept, Measurement of planar sets, Lebesgue measurement and its properties, Measurable functions, Convergences, Lebesgue integral properties, Lebesgue fatou and Levi theorems

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Sigma Algebra and Algebra Concepts
2	Axiom of Choice and the Infinite Direct Products
3	Countable sets
4	Real Number System
5	Open and Closed Sets
6	Borel Sets
7	Measurement and exterior Measurement Concepts
8	Midterm Exam
9	Measurement and exterior Measurement Concepts
10	Measurement and exterior Measurement Concepts
11	Measurement and exterior Measurement Concepts
12	Measurable sets and Lebesgue Measure
13	Measurable sets and Lebesgue Measure
14	Measurable sets and Lebesgue Measure
15	Clusters can not be measured
16	Final Exam

Recommended or Required Reading

H. L. Royden, Real Analysis, Macmillan Publishing Co. Inc., 1963. A. Mukherjea and K. Pothoven, Real and Functional Analysis, Plenum Press, 1984. M. Balcı, Real Analysis, Balcı Yayınları, 2000. A. Dönmez, Real Analysis, Seçkin Publishing, 2001.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Self Study	14	5	70
Individual Study for Mid term Examination	7	8	56
Individual Study for Final Examination	7	8	56
TOTAL WORKLOAD (hours)			186

Contribution of Learning Outcomes to Programme Outcomes

LO1

LO2

LO3

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High