Real Analysis : Elementary Sets and Closure
October 1st, 2022
1) Let M be an elementary set. Prove that | closure(M)M | = 0. (closure of M can also be written as M bar, and it is the union of M and limit points of M).
2) If M and N are elementary sets then show that
| M union N | + | M intersection N| = |M| + |N|
The definition of elementary set : If M is a union of finite members of disjoint cells, then M is said to be an elementary set.
I believe it is related to lebesgue measure topics, but not so sure.