A skeleton of calculus PS, PDF
Hint for problem 2c in Homework 8 PDF-file
Note that the "epsilon" in the first sub-bullet of the third bullet can be arbitrarily small. (That is, the statement should have been preceded by "For every strictly positive epsilon, show that ..")
In addition, the set A in this same sub-bullet also satisfies the condition that its Lebesgue-measure does not exceed that of E by more than epsilon.
Here is Homework 9
And here are the comments for Homework 7.