Real Function Theory

September 1, 2003 to January 9, 2004

Introduction to the Course of Real Function Theory

Chapter 1.  Cardinality of Set and Euclidean Space

Lecture 1. Cardinality of Set

Lecture 2. Countable and Uncountable Sets

Lecture 3. Euclidean Spaces

Chapter 2.  Measure of the sets in Euclidean Space

Lecture 1. Outer Measure

Lecture 2. Measurable Sets

Lecture 3. Review and Exercises

Lecture 4. Measure and Topology

Lecture 5. Further Discussion on Measurability

Lecture 6. Measure Under Transforms

　

Chapter 3.  Measurable Functions   

Lecture 1. Measurable Functions

Lecture 2. Structure of Measurable Functions

Lecture 3. Convergence in Measure

Chapter 4.  Integrals of Functions

Lecture 1. Definition of Integral

Lecture 2. Integrable functions 

Lecture 3. Function Spaces L and C

Lecture 4. Review and Exercises

Lecture 5. Evaluation of Integrals

Lecture 6. Review and Exercises

Lecture 7. Repeated Integration

Chapter 5.  Functions of Bounded Variation, Newton-Leibniz Forlmula

Lecture 1. Definition and Properties

Lecture 2. Monotone Functions

Lecture 3. Absolutely Continuous Functions

Levture 4. Convex Functions

Lecture 5. Review and Exercises

Lecture 6. Evaluation of Integrals

Lecture 7. Hardy-Littlewood Operator

Lecture 8. Review and Exercises

　

Undergraduate Seminar

Schedule