# MATH5011 - Real Analysis I - 2014/15

Course Name:
Course Year:
2014/15
Term:
1

### Announcement

• The finalized chapter 2 differs very few from the old version. Aside from correcting typos, I have added some explanatory words on pages 9 and 16.
• There are two changes in Chapter 3. First, notations in Proposition 3.3 have been improved. Second, the proof of Theorem 3.6 (d) is now removed.
• The coverage of midterm: Chapter 1, 2 and 3 (3.1 and 3.2 only).
• Attention for those who scored less than 60 in the midterm exam. To gain partial credits to improve you grade, you could hand in exercises beginning from Ex 8. Hand in Problems 1,2 and 4 in Ex 8 by next Monday (Nov 3).
• Those who would like to hand in Ex 9, please hand in #3, 5, 8, 10, 12 and 14 by Nov 17
• The final examination will be held on Nov 24 (4:30-6:30). The coverage is 3.4 (Proposition 3.10(c) excluded), 3.5, 4.1--4.5, and 5.1--5.3.
• A new Proposition 5.3 has been added with some minor changes.
• Explanations to some questions you guys asked me earlier. 1.  The outer regularity of the Hausdorff measure.  The definition of a regular Borel measure should follow the one in [EG].  Outer regularity means for each set $A$ there is a Borel set $B$ containing $A$ with the same measure.  $B$ is not nec open.  Please refer to theorem 1 in chapter 2 of [EG]. I will revise the notes later. 2.  In # 9(a), Ex 8, add the assumption $\|g\|_{1/q}$ is finite. 3.  In #13, Ex 9,  the first several sentences should be:  Suppose on the contrary that $\exists\eps_0>0$ such that $\forall n\in\N$, $\exists E_n\in\M$ with $\mu(E_n)<2^{-n}$ such that $\lambda(E_n)\geq \eps_0$. Put $\displaystyle E=\bigcap_{n\in\N}\bigcup_{k\geq n}E_k$. etc. There are a couple of typos. [Download file]

### General Information

#### Lecturer

• Prof Kai-Seng Chou
• Office: Rm 237 LSB
• Tel: 3943 7971
• Email:

#### Teaching Assistant

• Mr Tianwen Luo
• Office: Rm 614 Academic Building
• Tel: 3943 4109
• Email:
• Office Hours: Mon-Tue-Wed-Thu: 12:45-2:00pm

#### Time and Venue

• Lecture: M9-11, LSK 212

### 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.

### Assessment Scheme

 Midterm Examination (October 20, 2014) 50% Final Examination (November 24, 2014) 50%