I would like to get help with this question and be sure to show steps. It's a hard question, you don't have to solve it but please show me enough steps to this question

Problem 10.1.3. (Lebesgue Measure of Rectangles = Their Content) I Show that ((S) = 0 for any 5 = x e Rd such that x; = c - the d-1- dimensional plane obtained by holding the i-th coordinate constant. 2 Show that if u(D) = 0, then (CUD) = (C) 3 Show that the measure of any rectangle when some or all of the intervals defining it are not open is the same as the corresponding open rectangle. 4 Show that for any rectangle R C IRd C"(R) = c(R). Hint take the closed rectangle R corresponding to R and notice that any cover with open rectangles has a finite subcover also covering R. This is not a trivial exercise, so beware of trivial arguments