MATH5011 - Real Analysis I - 2021/22

Announcement

• Here is the course outline of Math5011 [Download file]
• Please upload the complete assignment (in PDF file) to Blackboard CUHK
• The teaching venue of Math 5011 has been changed to LSB, Room 222.

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General Information

Lecturer

• Prof. De-Jun Feng
  • Office: LSB 211
  • Tel: 39437965
  • Email:

Teaching Assistant

• Mr. Tian-Han Yi
  • Office: LSB G08
  • Tel: 3943 7954
  • Email:
  • Office Hours: Thursday, 9am–11am

Time and Venue

• Lecture: Fri 9:30AM - 12:15PM, LSB, Room 222

Course Description

Abstract integration theory; outer measures and Caratheodory's construction, Borel, Radon and Hausdorff measures; positive linear functionals and Riesz representation theorem; Lp-spaces and their functional properties; and signed measures, Radon-Nikodym theorem and the dual of the space of continuous functions.

References

• Real and Complex Analysis, 3rd ed. W. Rudin, McGraw-Hill, New York 1966.
• Measure Theory and Fine Properties of Functions, L.C. Evans and R.F. Gariepy, CRC Press 1992.
• Real Analysis: Measure Theory, Integration and Hilbert Spaces, E.M. Stein and R. Shakarchi, Princeton Lectures in Analysis, Princeton 2005.
• Real and Abstract Analysis, E. Hewitt and K. Stromberg, Graduate Texts in Mathematics, Springer-Verlag, New York 1975.

Lecture Notes

• Lecture notes (Chapter 1)
• Lecture notes (Chapter 2)
• Lecture notes (Chapter 3)
• Lecture notes (Chapter 4)
• Lecture notes (Chapter 5)

Assignments

• Exercise 1 (due date: 17/09/2021)
• Exercise 2 (due date: 24/09/2021)
• Exercise 3 (due date: 02/10/2021)
• Exercise 4 (due date: 15/10/2021)
• Exercise 5 (due date: 22/10/2021)
• Exercise 6 (due date: 05/11/2021)
• Exercise 7 (due date: 19/11/2021)
• Exercise 8 (due date: 26/11/2021)
• Exercise 9 (due date: 3/12/2021)
• Exercise 10 (due date: 8/12/2021)

Solutions

• Exercise 1 Sol
• Exercise 2 Sol
• Exercise 3 Sol
• Exercise 4 Sol
• Exercise 5 Sol
• Midterm Sol
• Exercise 6 Sol
• Exercise 7 Sol
• Exercise 8 Sol
• Exercise 9 Sol
• Exercise 10 Sol

Assessment Scheme

Assignments		10%
Mid-term Exam		45%
Final Exam		45%

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

http://www.cuhk.edu.hk/policy/academichonesty/

and thereby help avoid any practice that would not be acceptable.

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Assessment Policy

Last updated: December 03, 2021 10:43:00