Posted by Adi
on December 12, 2007, 12:42 am
On page 16, it says that despite obs 4 and 5, we CANNOT conclude in general that if E1 U E2 is a disjoint union of subsets of R^d, then m*(E1 U E2)= m*(E1) U m*(E2). Why is that?
Isn't that what obs 4 saying? The only requirement for obs 4 is that the two sets have distance greater than zero, isn't that equivalent to saying that they're disjoint?
Also related, in the proof of Thm 3.2 on p. 19, they said that for a fixed N, the sets F1, F2, ... FN are compact and disjoint, and this implies that m(U j=1..n Fj)= Sum j=1..N m(Fj). Why is the implication true?
Help?
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