advertisement

MATHEMATICS 420/507, PROBLEM SET 3 Due on Friday, October 23, 2015 Write clearly and legibly, in complete sentences. You may discuss the homework with other students, but the final write-up must be your own. If your solution uses any results not introduced in class, state the result clearly and provide either a reference or a proof. 1. Section 1.5, Problem 29. (10 marks, 5 for each part) 2. Section 2.1, Problem 1. (10 marks. The textbook defines measurable functions with values in R via Borel sets on R, see page 45. I used in class the definition given in this question. You are asked to verify that the two definitions are equivalent.) 3. Section 2.1, Problem 3. (10 marks) 4. Section 2.1, Problem 9. (30 marks. You can use all facts about the Cantor function that are stated and proved in Section 1.5, even if I did not mention them in class.) 1