National Tsing Hua University
Math 5131 - Real Analysis II
Homework Problems 

• Problems with asterisks * will be collected and graded. Assignments will be collected every Friday, unless announced otherwise. 

2/23:   Exercises 1.1, 1.3*, 1.4, 1.6* on Chapter 8 of Lecture Notes 

3/2:   Exercises 2.1, 2.2*, 2.3*, 2.4, 2.5 on Chapter 8 of Lecture Notes 

3/9:   Exercises 3.1, 3.2*, 3.3, 3.4, 3.5*, 3.6*, 3.7*, 3.8 on Chapter 8 of Lecture Notes 

3/16:   Exercises 4.1, 4.2*, 4.3*, 4.4*, 4.5* on Chapter 8 of Lecture Notes 

3/23:   Exercises 5.1, 5.2*, 5.3*, 5.4, 6.1, 6.2* on Chapter 8 of Lecture Notes 

3/31:   Exercises 6.1, 6.2, 6.3, 6.4*, 6.5 on Chapter 8 of Lecture Notes, Exercises 4.2, 4.5, 4.10*, 4.15*, 4.19 (in textbook)

4/20 & 27:  Exercises 4.7*, 4.8, 4.11, 4.12*, 4.22, 4.24* 

5/4:  Exercises 4.9*, 4.16*, 4.17 

5/25:  Exercises 6.2, 6.11*, 6.12, 6.13 
Need the following definitions:
(1) A measure space is complete if the σ-algebra contains every subset of measure zero sets. (so Lebesgue measure is complete, recall page 17 of the textbook.)
(2) Let m be the Lebesgue measure. Given nonnegative Borel measurable function f, the measure μ defined by μ(E) = ∫_E f dm is the measure associated to f.

6/1:  Exercises 1, 2*, 3, 4*, 5, 6  in "Some Exercises for Abstract Measures"

Erratum for lecture notes

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