Enquiry for Science Major/Minor/Programme Requirements
MATH7505 Real analysis (6 credits) Academic Year 2025
Offering Department Mathematics Quota ---
Course Co-ordinator Prof C Y Hui, Mathematics < chhui@maths.hku.hk >
Teachers Involved (Prof C Y Hui,Mathematics)
Course Objectives To introduce the basic ideas and techniques of measure theory and the Lebesgue integral.
Course Contents & Topics • Lebesgue Measure on R: Measurable Sets and Lebesgue Measure, Measurable Functions.
• The Lebesgue Integral: The Lebesgue Integral, Modes of Convergence, Convergence Theorems.
• Differentiation and Integration: Functions of Bounded Variation, Differentiation of an Integral, Absolute Continuity.
• The L^p Spaces: The L^p spaces, Convergence and Completeness, Bounded Linear Functionals.
• General Theory: Measurable Spaces, Measurable Functions, Integration, Convergence Theorems, Radon-Nikodym Theorem.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 describe basic properties of Lebesgue measure and measurable functions and understand and apply various convergence theorems
CLO 2 construct the Lebesgue integral, elucidate its basic properties and appreciate the existence of other useful integration theories besides Riemann's
CLO 3 understand the basic properties of L^p spaces
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 1. Pass in MATH3401.  
2. MATH3541 recommended but not required.
Course Status with Related Major/Minor /Professional Core 2025 Major in Mathematics ( Disciplinary Elective )
2025 Major in Mathematics (Intensive) ( Disciplinary Elective )
2025 Minor in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics (Intensive) ( Disciplinary Elective )
2024 Minor in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics (Intensive) ( Disciplinary Elective )
2023 Minor in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics (Intensive) ( Disciplinary Elective )
2022 Minor in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics (Intensive) ( Disciplinary Elective )
2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping 2025 Major in Mathematics < PLO 1,2,3 >
2025 Major in Mathematics (Intensive) < PLO 1,2,3 >
2024 Major in Mathematics < PLO 1,2,3 >
2024 Major in Mathematics (Intensive) < PLO 1,2,3 >
2023 Major in Mathematics < PLO 1,2,3 >
2023 Major in Mathematics (Intensive) < PLO 1,2,3 >
2022 Major in Mathematics < PLO 1,2,3 >
2022 Major in Mathematics (Intensive) < PLO 1,2,3 >
2021 Major in Mathematics < PLO 1,2,3 >
2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026 Y        2nd sem    Examination May     
Offer in 2026 - 2027 Y
Course Grade A+ to F
Grade Descriptors
A Demonstrate a thorough understanding of all concepts and ideas by being able to draw complex connections among various concepts and apply the theorems through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation, and with some innovative approaches to solving problems.
B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, reasoning, identifying the appropriate theorems, applications, or presentation.
C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with acceptable argument and presentation.
D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation.
Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, and not being able to complete the solution.
Communication-intensive Course N
Course Type Lecture-based course
Course Teaching
& Learning Activities
Activities Details No. of Hours
Lectures 36.0
Reading / Self study 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments 20.0 1,2,3
Examination Written 50.0 1,2,3
Test Written / Oral 30.0 1,2,3
Required/recommended reading
and online materials		 1. Axler: Measure, Integration, and Real Analysis
2. Folland: Real Analysis
3. Folland: A Guide to Advanced Real Analysis
4. Royden: Real Analysis
5. Rudin: Real and complex analysis
6. Stein and Shakarchi: Real Analysis
Course Website http://moodle.hku.hk/
Additional Course Information


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