Math 318 HW #6
Due 5:00 PM Thursday, March 17
Reading:
Wilcox & Myers §13–15.
Problems:
1. (a) Exercise 16.7.
(b) Exercise 16.36.
2. Exercise 16.23.
3. (a) Find a trivial proof of Theorem 12.9 which illustrates why this theorem is not very useful
as stated.
(b) Prove the following, actually useful, version of Theorem 12.9: Given a measurable set
A ⊆ [0, 1], there exists a Borel set B ⊆ [0, 1] such that the symmetric difference A4B
has measure zero.
(Recall that the symmetric difference of two sets is defined as A4B = (A\B) ∪ (B\A).)
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